Fluid Mechanics for Engineers in SI Units

David A Chin

Chapter 1

Properties of Fluids - all with Video Answers

Educators

Chapter Questions

Problem 1

The lift force, $F_{\mathrm{L}}[\mathrm{F}],$ exerted on an object with a plan area $A\left[\mathrm{~L}^{2}\right]$ by a fluid with an approach velocity $V\left[\mathrm{LT}^{-1}\right]$ and density $\rho\left[\mathrm{ML}^{-3}\right]$ is usually derived using the relation
$$
F_{\mathrm{L}}=C_{\mathrm{L}} \frac{1}{2} \rho V^{2} A
$$
where $C_{\mathrm{L}}$ is an empirical constant called the lift coefficient.
(a) What are the units of $C_{\mathrm{L}}$ if standard SI units are used for $F_{\mathrm{L}}, \rho, V,$ and $A ?(\mathrm{~b})$ What adjustment factor would be applied to $C_{\mathrm{L}}$ if standard USCS units were used for $F_{\mathrm{L}}, \rho, V,$ and $A ?$

Kudakwashe Mapiki

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Problem 2

A force balance in a particular fluid flow is combined with Newton's second law to yield the equation
$$
\rho \frac{\mathrm{d}^{2} z}{\mathrm{~d} t^{2}}+a \frac{\mathrm{d} z}{\mathrm{~d} t}+b z=c
$$
where $\rho, z,$ and $t$ are dimensional variables with the following dimensions: $\rho\left[\mathrm{ML}^{-3}\right],$ $z[\mathrm{~L}],$ and $t[\mathrm{~T}]$. (a) Determine the dimensions of the system parameters $a, b,$ and $c .$
(b) If standard SI units are to be used in the given equation and values of $\rho, z,$ and $t$ are provided in $\mathrm{g} / \mathrm{cm}^{3}, \mathrm{~mm},$ and $\mathrm{h}$, respectively, what conversion factors must be applied to these variables before they are used in the equation?

Kudakwashe Mapiki

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Problem 3

An equation that is commonly used to describe the volume flow rate of water in an open channel is given by
$$
Q=\frac{1}{n} \frac{A^{\frac{5}{3}}}{P^{\frac{2}{3}}} S_{0}^{\frac{1}{2}}
$$
where $Q$ is the volume flow rate in the channel $\left[\mathrm{L}^{3} \mathrm{~T}^{-1}\right], n$ is a constant that characterizes the roughness of the channel surface [dimensionless], $A$ is the flow area $\left[\mathrm{L}^{2}\right]$, $P$ is the perimeter of the flow area that is in contact with the channel boundary [L], and $S_{0}$ is the slope of the channel [dimensionless]. This equation is usually applied using SI units, where $Q$ is in $\mathrm{m}^{3} / \mathrm{s}, A$ is in $\mathrm{m}^{2},$ and $P$ is in $\mathrm{m}$. (a) Is the given equation dimensionally homogeneous? (b) If the equation is not dimensionally homogeneous, what conversion factor must be inserted after the equal sign for the equation to work with $Q$ in $\mathrm{ft}^{3} / \mathrm{s}, A$ in $\mathrm{ft}^{2},$ and $P$ in $\mathrm{ft}$ ?

Kudakwashe Mapiki

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Problem 4

Give the dimensions and typical SI units of the following quantities commonly used in engineering: energy, force, heat, moment, momentum, power, pressure, strain, stress, and work.

Kudakwashe Mapiki

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Problem 5

Use prefixes to express the following quantities with magnitudes in the range of $0.01-1000:($ a $) 6.27 \times 10^{7} \mathrm{~N},$ (b) $7.28 \times 10^{5} \mathrm{~Pa},$ (c) $4.76 \times 10^{-4} \mathrm{~m}^{2},$ and (d) $8.56 \times$ $10^{5} \mathrm{~m}$.

Kudakwashe Mapiki

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Problem 6

Convert the following quantities to SI units: 15 gallons per minute, 99 miles per hour, 20 feet per second, 150 cubic feet per minute, 1540 gallons, 28 acres, and 600 horsepower.

Kudakwashe Mapiki

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Problem 7

Derive the following conversion factors: (a) horsepower to watts and (b) pounds per square inch to pascals.

Kudakwashe Mapiki

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Problem 8

What is the largest percentage error in the density of liquid water that can be made if the density is always assumed to be equal to $990 \mathrm{~kg} / \mathrm{m}^{3}$ ?

Kudakwashe Mapiki

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Problem 9

If $4 \mathrm{~L}$ of a liquid with density $1020 \mathrm{~kg} / \mathrm{m}^{3}$ is mixed with $6 \mathrm{~L}$ of a liquid with density $940 \mathrm{~kg} / \mathrm{m}^{3},$ what is the density of the mixture?

Kudakwashe Mapiki

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Problem 10

(a) What is the specific weight of water at $0^{\circ} \mathrm{C}, 20^{\circ} \mathrm{C},$ and $100^{\circ} \mathrm{C} ?$
(b) What is the specific gravity of water at $0^{\circ} \mathrm{C}, 20^{\circ} \mathrm{C},$ and $100^{\circ} \mathrm{C} ?$

Kudakwashe Mapiki

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Problem 11

A 450-L storage tank is completely filled with water at $25^{\circ} \mathrm{C}$. (a) If the top of the storage tank is left open to the atmosphere and the water in the tank is heated to $80^{\circ} \mathrm{C},$ what volume of water will spill out of the tank? (b) If the water is cooled back down to $25^{\circ} \mathrm{C}$, by what percentage will the weight of water in the tank be reduced from its original weight? Neglect the expansion of the tank when the water is heated.

Kudakwashe Mapiki

Kudakwashe Mapiki

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Problem 12

If the specific weight of a substance is $15 \mathrm{kN} / \mathrm{m}^{3},$ what is its density and specific gravity?

Kudakwashe Mapiki

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Problem 13

If the specific gravity of a substance is $2.5,$ what is its density and specific weight?

Kudakwashe Mapiki

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Problem 14

The concentration of a dissolved or suspended substance in a liquid is commonly expressed as the ratio of the mass of the substance to the mass of the mixture of the liquid and the substance. The concentration unit of parts per million (ppm) is an example of such a ratio. Determine the relationship between the mass ratio, the specific gravity of the pure liquid, and the specific gravity of the mixture.

Kudakwashe Mapiki

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Problem 15

If the density of a substance is $810 \mathrm{~kg} / \mathrm{m}^{3},$ what is its specific gravity and its specific weight?

Kudakwashe Mapiki

Kudakwashe Mapiki

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Problem 16

A storage reservoir contains $250 \mathrm{~kg}$ of a liquid that has a specific gravity of $2 .$ What is the volume of the storage reservoir?

Kudakwashe Mapiki

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Problem 17

An empty container weighs $10 \mathrm{~N},$ and when filled with kerosene at $20^{\circ} \mathrm{C},$ it weighs $50 \mathrm{~N}$. Estimate the volume of kerosene required to fill the container. What is the mass of kerosene required to fill the container?

Kudakwashe Mapiki

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Problem 18

Show that the relationship between the bulk modulus and the fractional change in density, as given by Equation $1.13,$ can be derived from the definition of the bulk modulus in terms of the volumetric strain, as given by Equation 1.12 .

Kudakwashe Mapiki

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Problem 19

What magnitude of pressure change would be necessary to change the density of water by $1 \%$ at $20^{\circ} \mathrm{C} ?$

Kudakwashe Mapiki

Kudakwashe Mapiki

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Problem 20

Water at $20^{\circ} \mathrm{C}$ is pumped into a spherical tank of diameter $3 \mathrm{~m},$ and pumping is stopped when the water just fills the tank. The tank manufacturer claims that the tank can withstand an internal gauge pressure of up to $9 \mathrm{MPa}$ and that the deformation of the tank is negligible for pressures up to $9 \mathrm{MPa}$. What additional mass of water could be pumped into the tank and still maintain the integrity of the tank?

Anand Jangid

Numerade Educator

Problem 21

As the pressure in a liquid reservoir is increased from $150 \mathrm{kPa}$ to $28000 \mathrm{kPa}$, the volume of liquid in the reservoir decreases from $1.500 \mathrm{~m}^{3}$ to $1.450 \mathrm{~m}^{3}$. Estimate the bulk modulus of the liquid.

Kudakwashe Mapiki

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Problem 22

The pressure on $10 \mathrm{~m}^{3}$ of benzene at $20^{\circ} \mathrm{C}$ is increased by $10 \mathrm{MPa}$. Estimate the expected change in the volume of benzene.

Kudakwashe Mapiki

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Problem 23

Water at $20^{\circ} \mathrm{C}$ is poured into a pot and brought to a boiling point at $100^{\circ} \mathrm{C}$ at a constant atmospheric pressure of $101.3 \mathrm{kPa}$. (a) Use the coefficient of volume expansion to estimate the percentage change in the density of the water. (b) Estimate the percentage change in the depth of water in the pot.

Kudakwashe Mapiki

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Problem 24

Ethylene glycol, which is commonly used as a coolant in car radiators, has a coefficient of volume expansion of around $5.7 \times 10^{-4} \mathrm{~K}^{-1}$. Estimate the percentage change in density when the temperature of ethylene glycol is raised from $10^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$. Assume that the pressure remains constant.

Kudakwashe Mapiki

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Problem 25

A plastic container is completely filled with gasoline at $15^{\circ} \mathrm{C}$. The container specifications indicate that it can endure a $1 \%$ increase in volume before rupturing. Within the temperatures likely to be experienced by the gasoline, the average coefficient of volume expansion of gasoline is $9.5 \times 10^{-4} \mathrm{~K}^{-1}$. Estimate the maximum temperature rise that can be endured by the gasoline without causing a rupture in the storage container.

Kudakwashe Mapiki

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Problem 26

Compare the speed of sound in mercury with the speed of sound in air. Assume that both liquids are at $20^{\circ} \mathrm{C}$.

Kudakwashe Mapiki

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Problem 27

Measurements indicate that the acoustic velocity in a dense liquid is $1800 \mathrm{~m} / \mathrm{s}$. If the specific gravity of the liquid is $1.9,$ what is the bulk modulus of the liquid?

Kudakwashe Mapiki

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Problem 28

The limiting condition for the continuum approximation to be applicable in an ideal gas is sometimes defined as the condition at which the gas contains less than $10^{10}$ molecules per $\mathrm{mm}^{3}$. (a) For an ideal gas in which the temperature is $15^{\circ} \mathrm{C}$, what will be the pressure at the limiting condition? Take into consideration that Avogadro's number is $6.023 \times 10^{23}$ molecules/mole. (b) What term is used to describe a gas in which the continuum approximation is not valid?

Kudakwashe Mapiki

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Problem 29

Compare the density of helium to the density of air at a pressure of $101 \mathrm{kPa}$ and a temperature of $25^{\circ} \mathrm{C}$. What are the specific volumes of these two gases at the given temperature and pressure?

Kudakwashe Mapiki

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Problem 30

Air is commonly assumed to be an ideal gas; in addition, the properties of air are frequently obtained from tabulated values. Compare the densities of air at temperatures in the range of -40 to $1000^{\circ} \mathrm{C}$ at standard atmospheric pressure as given in Appendix B.2 with the densities estimated using the ideal gas law. Based on your results, assess the accuracy of estimating the air density at atmospheric pressure using the ideal gas law.

Kudakwashe Mapiki

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Problem 31

If pure oxygen is compressed such that its density and pressure are $5 \mathrm{~kg} / \mathrm{m}^{3}$ and $450 \mathrm{kPa}$, respectively, estimate the temperature of the oxygen.

Kudakwashe Mapiki

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Problem 32

A steel tank is filled with helium at a temperature of $17^{\circ} \mathrm{C}$ and a pressure of $550 \mathrm{kPa}$. If the tank has a volume of $3 \mathrm{~m}^{3}$, what is the mass, density, and weight of helium in the tank?

Kudakwashe Mapiki

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Problem 33

A steel tank is to be sized to contain $12 \mathrm{~kg}$ of pure oxygen at a temperature of $27^{\circ} \mathrm{C}$ and a pressure of $15 \mathrm{MPa}$. It is desired that the tank have a cylindrical shape, with a length that is three times its diameter. What are the required dimensions of the tank?

Kudakwashe Mapiki

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Problem 34

The mass of air in a tank is estimated as $12 \mathrm{~kg},$ and the temperature and pressure of the air in the tank are measured as $67^{\circ} \mathrm{C}$ and $210 \mathrm{kPa}$, respectively. Estimate the volume of air in the tank.

Kudakwashe Mapiki

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Problem 35

The mass of compressed air in a 210 -L steel tank is determined by weighing the tank plus its contents and then subtracting the known weight of the empty tank. The mass of compressed air in the tank is found to be equal to $3.2 \mathrm{~kg}$. If the tank is located in a room where the temperature is maintained at $25^{\circ} \mathrm{C}$, estimate the pressure of the air in the tank.

Kudakwashe Mapiki

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Problem 36

A $0.1-\mathrm{m}^{3}$ tank is filled with air at a temperature and pressure of $20^{\circ} \mathrm{C}$ and $400 \mathrm{kPa}$, respectively. What is the weight of air in the tank?

Kudakwashe Mapiki

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Problem 37

A large classroom is $10 \mathrm{~m}$ wide and $12 \mathrm{~m}$ long, and the distance from the floor to the ceiling is $4 \mathrm{~m} .$ The air in the room is at standard atmospheric pressure, and the temperature in the room is $20^{\circ} \mathrm{C}$. (a) Estimate the mass of air (in $\mathrm{kg}$ ) and the weight of air (in $\mathrm{kN}$ ) in the room. (b) If the room is cooled down to $10^{\circ} \mathrm{C}$, what is the percentage change in the mass of air in the room?

Kudakwashe Mapiki

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Problem 38

A steel tank contains air at a temperature and pressure of $20^{\circ} \mathrm{C}$ and $600 \mathrm{kPa}$, respectively. If the temperature of the air in the tank increases to $30^{\circ} \mathrm{C},$ what is the change in pressure? What would be the change in pressure if the gas in the tank were helium?

Kudakwashe Mapiki

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Numerade Educator

Problem 39

A car tire has low air pressure at $130 \mathrm{kPa}$, and the pressure needs to be raised to 210 $\mathrm{kPa}$. If the volume of the tire is $15 \mathrm{~L}$ and the temperature of the air in the tire is $30^{\circ} \mathrm{C}$ estimate the mass of air that needs to be added. Assume that the air temperature and the volume of the tire remain constant.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 40

A car tire has a volume of $20 \mathrm{~L}$ and has a recommended (gauge) inflation pressure of $210 \mathrm{kPa}$ at a temperature of $25^{\circ} \mathrm{C}$. (a) If driving on the highway on a hot day causes the temperature of the air in the tire to increase to $65^{\circ} \mathrm{C},$ what will be the (gauge) air pressure in the tire? (b) If under the condition in part (a) air is let out of the tire to restore the tire pressure to $210 \mathrm{kPa}$, what will be the (gauge) air pressure in the tire when the air cools down to $25^{\circ} \mathrm{C}$ ? Assume that the tire volume remains constant and that atmospheric pressure is $101.3 \mathrm{kPa}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 41

The National Football League (NFL) requires that footballs used in games be inflated to a pressure in the range of $86.2-93.1 \mathrm{kPa}$. In a 2015 playoff game between the New England Patriots and the Indianapolis Colts, the footballs used in the game were inflated in a room with an air temperature of $20^{\circ} \mathrm{C} ;$ at game time, the temperature on the field was recorded as $10^{\circ} \mathrm{C}$. Upon checking the footballs prepared by the New England Patriots, the referees found that the pressures in the footballs were only around $72.4 \mathrm{kPa}$. Atmospheric pressure can be assumed to have been approximately $101.4 \mathrm{kPa}$. (a) What is the minimum pressure that would be expected in the footballs if only the temperature change is taken into account? (b) What on-field temperature would be required for the pressure in the footballs to be $72.4 \mathrm{kPa} ?$ (c) Propose a theory of how the pressures in the footballs ended up being $72.4 \mathrm{kPa}$. Assume that the volume of a football does not change significantly for pressures in the range of $72.4-93.1 \mathrm{kPa}$

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 42

Before embarking on a 40-minute drive on the highway, a motorist adjusts his tire pressure to $207 \mathrm{kPa}$. At the end of his trip, the motorist measures his tire pressure as $241 \mathrm{kPa}$. Assume that the volume of the tire remains constant during the trip. (a) Estimate the percentage increase in the temperature of the air in the tire. (b) If the initial temperature of the air in the tire is assumed to be equal to the ambient air temperature of $25^{\circ} \mathrm{C},$ what is the estimated temperature of the air in the tire at the end of the trip.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 43

(a) A spherical balloon with a diameter of $8 \mathrm{~m}$ is filled with helium at $22^{\circ} \mathrm{C}$ and 210 $\mathrm{kPa}$. Determine the number of moles and the mass of helium in the balloon. (b) When the air temperature in an automobile tire is $27^{\circ} \mathrm{C},$ the pressure gauge reads $215 \mathrm{kPa}$. If the volume of the tire is $0.030 \mathrm{~m}^{3},$ determine the pressure rise in the tire when the air temperature in the tire rises to $53^{\circ} \mathrm{C}$. (Note: Volume of a sphere is $\pi D^{3} / 6 ;$ relative molecular mass of He is 4.003 ; universal gas constant, $R_{\mathrm{u}}$, is 8312 $\mathrm{J} / \mathrm{kmol} \cdot \mathrm{K} .$ )

Kudakwashe Mapiki

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Problem 44

A helium balloon is to be used to lift a lab rat that weighs $1.5 \mathrm{~N}$. The density of the air is $1.17 \mathrm{~kg} / \mathrm{m}^{3}$, atmospheric pressure is $100 \mathrm{kPa}$, the air temperature is $25^{\circ} \mathrm{C},$ and the balloon weighs $0.5 \mathrm{~N}$. What mass of helium (in kilograms) must be put in the balloon to lift the rat?

Kudakwashe Mapiki

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Numerade Educator

Problem 45

Consider the case of an air bubble released from the bottom of a $12-\mathrm{m}$ -deep lake as shown in Figure 1.21 . The bubble is filled with air, it has an initial diameter of $6 \mathrm{~mm},$ no air is lost or gained in the bubble as it rises, and the air in the bubble and the surrounding lake water maintain a constant temperature of $20^{\circ} \mathrm{C}$. Atmospheric pressure, $p_{\mathrm{atm}},$ on the surface of the lake is $101.3 \mathrm{kPa},$ and the pressure, $p,$ at any depth, $z$, below the surface of the lake is given by $p=p_{\text {atm }}+\gamma z$, where $\gamma$ is the specific weight of the water in the lake. Estimate the diameter of the bubble when it surfaces.

Kudakwashe Mapiki

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Numerade Educator

Problem 46

A $1.1-\mathrm{m}^{3}$ volume of air at a pressure of $101 \mathrm{kPa}$ is compressed to a volume of $0.45 \mathrm{~m}^{3} .$ (a) What is the pressure in the compressed volume if the compression process is isentropic? (b) What is the pressure if the compression process is isothermal?

Kudakwashe Mapiki

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Numerade Educator

Problem 47

The atmospheric pressure in dry air at $20^{\circ} \mathrm{C}$ is $101.3 \mathrm{kPa},$ and a sample of the air indicates that it is $20 \%$ oxygen $\left(\mathrm{O}_{2}\right)$ and $80 \%$ nitrogen $\left(\mathrm{N}_{2}\right)$ by volume. (a) Estimate the partial pressure of $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$ in the air. (b) Estimate the density of the air.

Kudakwashe Mapiki

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Numerade Educator

Problem 48

A $2.0-\mathrm{m}^{3}$ volume of pure oxygen at a temperature and pressure of $20^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, respectively, is expanded to a volume of $4.0 \mathrm{~m}^{3} .$ (a) What is the pressure in the expanded volume if the expansion process is isentropic? What are the initial and final densities of the gas? (b) What is the pressure in the expanded volume if the expansion process is isothermal? What are the initial and final densities of the gas? (c) For the expansion process described in part (b), what amount of heat must be added to the gas?

Kudakwashe Mapiki

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Numerade Educator

Problem 49

Air flows into the nozzle shown in Figure $1.22,$ where the inflow air has a temperature and pressure of $27^{\circ} \mathrm{C}$ and $101 \mathrm{kPa}$, respectively, and the outflow air has a temperature of $-73^{\circ} \mathrm{C}$. Flow within the nozzle can be assumed to be adiabatic and frictionless. Estimate the pressure and density of the air exiting the nozzle.

Kudakwashe Mapiki

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Problem 50

A cylinder contains $0.3 \mathrm{~m}^{3}$ of air at $20^{\circ} \mathrm{C}$ and $120 \mathrm{kPa}$ pressure. With a piston mechanism, the air in the cylinder is compressed isentropically to a pressure of $700 \mathrm{kPa}$. What is the temperature of the air after compression?

Kudakwashe Mapiki

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Problem 51

A siren emits sound waves to alert people in the surrounding community of the occurrence of a tornado. If the temperature of the air is $22^{\circ} \mathrm{C}$, approximately how long does it take the sound to travel $1.1 \mathrm{~km} ?$

Kudakwashe Mapiki

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Problem 52

Compare the speed of sound in pure hydrogen with the speed of sound in air. Assume that both gases are at $20^{\circ} \mathrm{C}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 53

Remote measurements of the properties of a mystery gas find that the molecular weight of the gas is $35 \mathrm{~g} / \mathrm{mol}$ and the specific heat of the gas at constant pressure is $1025 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$. Estimate the speed of sound in this gas at a temperature of $22{ }^{\circ} \mathrm{C}$. Assume that the behavior of the gas can be approximated by that of an ideal gas.

Kudakwashe Mapiki

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Numerade Educator

Problem 54

Use the standard atmosphere to estimate the temperature and pressure at the top of Mount Everest, which is approximately $8840 \mathrm{~m}$ above sea level. Compare your estimated values with values reported in the open literature.

Kudakwashe Mapiki

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Numerade Educator

Problem 55

(a) Use the air density profile in the standard atmosphere as given in Appendix $\mathrm{B} .3$ to estimate the weight of air above $1 \mathrm{~m}^{2}$ of Earth's surface at sea level. (b) Use this result to estimate the pressure exerted on the surface of Earth by the standard atmosphere and compare this result with the conventional sea-level atmospheric pressure of $101.3 \mathrm{kPa}$. Explain the extent to which these pressures are in agreement. (c) If the total mass of air above $1 \mathrm{~m}^{2}$ was placed in a rectangular box with a base area of $1 \mathrm{~m}^{2}$ and the air in the box was at standard sea-level temperature and pressure, what would be the height of the box?

Kudakwashe Mapiki

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Numerade Educator

Problem 56

The lowest pressures at sea level are generally associated with hurricanes and tornados, and the lowest recorded pressure generated by any of these natural phenomena is reported to be $87.06 \mathrm{kPa}$. What elevation within the standard atmosphere would have this same pressure?

Kudakwashe Mapiki

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Numerade Educator

Problem 57

The summit of Mount Rainier (in Washington) experiences an average high temperature of $-7.2^{\circ} \mathrm{C}$ and an average low temperature of $-15^{\circ} \mathrm{C}$. Compare this range of temperatures with the temperature expected in the standard atmosphere. What is the expected atmospheric pressure on the summit of Mount Rainier?

Kudakwashe Mapiki

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Numerade Educator

Problem 58

Compare the mass of oxygen per unit volume of air at sea level with the corresponding value at a mountain resort at an elevation of $3000 \mathrm{~m} .$ If a person takes in the same volume of air with each breath and breathes at the same rate, what percentage reduction in oxygen is the person inhaling at the mountain resort? Assume a standard atmosphere.

Kudakwashe Mapiki

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Numerade Educator

Problem 59

A Boeing 777 aircraft has windows of dimension $270 \mathrm{~mm} \times 380 \mathrm{~mm}$, and the cabin pressure during flight is typically controlled at around $100 \mathrm{kPa}$. If the aircraft is cruising at an altitude of $11 \mathrm{~km}$, estimate the net force on each window.

Kudakwashe Mapiki

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Numerade Educator

Problem 60

The Boeing 787 Dreamliner has a design cruising speed of $913 \mathrm{~km} / \mathrm{h}$ at an altitude of $10700 \mathrm{~m}$. Assuming a standard atmosphere, what is the Mach number at which the aircraft flies under cruising conditions? Should the compressibility of air be taken into account in modeling the flight of this aircraft? Explain.

Kudakwashe Mapiki

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Numerade Educator

Problem 61

A research aircraft with sensitive external instrumentation has a design cruising speed of $885 \mathrm{~km} / \mathrm{h}$ and must not fly with a Mach number greater than 0.85 to avoid compressibility effects compromising the functioning of the instrumentation. Estimate the maximum altitude at which this aircraft should cruise.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 62

Tabulate the kinematic viscosity of water, $\nu$, as a function of temperature.

Kudakwashe Mapiki

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Numerade Educator

Problem 63

A fluid with a specific gravity of 0.92 has a kinematic viscosity of $5 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s}$ What is the dynamic viscosity of the fluid?

Kudakwashe Mapiki

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Problem 64

Methane at a temperature of $25^{\circ} \mathrm{C}$ and pressure of $110 \mathrm{kPa}$ has a dynamic viscosity of $12 \mu \mathrm{Pa} \cdot \mathrm{s}$. Estimate the kinematic viscosity at this same temperature and pressure.

Kudakwashe Mapiki

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Numerade Educator

Problem 65

Benzene at a temperature of $20^{\circ} \mathrm{C}$ flows at a high speed over a smooth flat plate and exerts a shear stress of $0.5 \mathrm{~Pa}$ on the plate. Estimate the velocity gradient at the surface of the plate and the velocity $2 \mathrm{~mm}$ away from the surface.

Kudakwashe Mapiki

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Numerade Educator

Problem 66

A fluid with a viscosity of $0.300 \mathrm{~Pa}$.s flows between parallel plates as illustrated in Figure $1.23 .$ The top and bottom plates each have an area of $1.5 \mathrm{~m}^{2},$ and the distance between the plates is $200 \mathrm{~mm}$. The distribution of velocity within the fluid is given by
$$
u=0.8\left(1-100 y^{2}\right)
$$
where $u$ is the velocity in $\mathrm{m} / \mathrm{s}$ and $y$ is the distance from the centerline in meters. (a) Determine the shear stress on the top and bottom plates. (b) Determine the shear forces exerted by the fluid on the top and bottom plates.

Kudakwashe Mapiki

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Numerade Educator

Problem 67

A lubricant is contained between two concentric cylinders over a length of $1.3 \mathrm{~m}$. The inner cylinder has a diameter of $60 \mathrm{~mm}$, and the spacing between the cylinders is $0.6 \mathrm{~mm}$. If the lubricant has a dynamic viscosity of $0.82 \mathrm{~Pa} \cdot \mathrm{s},$ what force is required to pull the inner cylinder at a velocity of $1.7 \mathrm{~m} / \mathrm{s}$ along its axial direction? Assume that the outer cylinder remains stationary and that the velocity distribution between the cylinders is linear.

Kudakwashe Mapiki

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Numerade Educator

Problem 68

A fluid is constrained between two $75-\mathrm{cm}$ -long concentric cylinders, where the diameter of the inner cylinder is $15 \mathrm{~cm}$ and the diameter of the outer cylinder is 15.24 $\mathrm{cm} .$ The inner cylinder rotates at $200 \mathrm{rpm},$ and the viscosity of the fluid is 0.023 Pa.s. (a) Determine the force that is exerted on the outer cylinder. (b) Determine the torque and power needed to rotate the inner cylinder.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 69

A viscometer is constructed with two $30-\mathrm{cm}$ -long concentric cylinders, one $20.0 \mathrm{~cm}$ in diameter and the other $20.2 \mathrm{~cm}$ in diameter. A torque of $0.13 \mathrm{~N} \cdot \mathrm{m}$ is required to rotate the inner cylinder at $400 \mathrm{rpm} .$ Calculate the viscosity of the fluid.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 70

SAE 30 oil at $20^{\circ} \mathrm{C}$ is contained within the 2 -mm space between a rotating cylinder and a fixed cylindrical reservoir as shown in Figure $1.24 .$ If the 0.5 -m-diameter rotating cylinder is required to turn at a rate of $3 \mathrm{rpm},$ what torque is required to rotate the cylinder?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 71

A cylinder with a mass of $0.8 \mathrm{~kg}$, a diameter of $50 \mathrm{~mm}$, and a length of $10 \mathrm{~cm}$ is to be dropped down a shaft of diameter $53 \mathrm{~mm}$ as shown in Figure $1.25 .$ The annular region between cylinders is filled with SAE 30 oil having a viscosity of $0.29 \mathrm{~Pa} \cdot \mathrm{s}$. The inner cylinder is dropped with an initial velocity of zero and ultimately achieves a constant speed called the terminal speed. (a) Determine the terminal speed. (b) Determine the time required to attain the terminal speed.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 72

A 0.4-mm-diameter cable is to be pulled through a 1.2 -mm-diameter glycerin-filled cavity as shown in Figure $1.26 .$ The glycerin to be used has a dynamic viscosity of $1.5 \mathrm{~Pa} \cdot \mathrm{s},$ and the cable can resist a $84-\mathrm{N}$ tensile force before it begins to fail. If the cable is to be pulled at a velocity of $1.3 \mathrm{~m} / \mathrm{s}$, what is the maximum length of the cavity that can be used to avoid tensile failure in the cable? Assume that the cable can be kept at the center of the cavity.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 73

A flat plate with an area of $1.7 \mathrm{~m}^{2}$ is moved at a velocity of $1.5 \mathrm{~m} / \mathrm{s}$ over a stationary plate as shown in Figure 1.27 . Two lubricants are contained in the 0.7 -mm space between the plates. The bottom 0.4 mm contains a lubricant with a dynamic viscosity of $0.2 \mathrm{~Pa} \cdot \mathrm{s},$ and the top $0.3 \mathrm{~mm}$ contains a lubricant with a dynamic viscosity of $0.3 \mathrm{~Pa} \cdot \mathrm{s}$. (a) What is the velocity at the interface between the two lubricants? (b) What force is required to move the top plate?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 74

A thin plate is pulled at a speed of $9 \mathrm{~m} / \mathrm{s}$ between two fixed stationary plates as shown in Figure 1.28 . Lubrication for the moving plate is provided by SAE 50 oil at $20^{\circ} \mathrm{C}$. The moving plate is $1 \mathrm{~m}$ long and $1.28 \mathrm{~m}$ wide, and the spacings between the top and bottom plates are $40 \mathrm{~mm}$ and $25 \mathrm{~mm}$, respectively. Estimate the force required to move the plate.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 75

Water at $20^{\circ} \mathrm{C}$ flows down the inclined channel shown in Figure $1.29,$ where the velocity distribution is given by
$$
u=1.2 y(1-y)
$$
where $u$ is the velocity in $\mathrm{m} / \mathrm{s}$ and $y$ is the distance from the bottom of the channel in meters. What is the magnitude of the shear stress exerted by the flowing water on the bottom of the channel?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 76

A block of weight $W$ slides down an inclined plane that is lubricated by a thin film of oil as shown in Figure 1.30 . The film contact area is $A,$ and its thickness is $h .$ Assuming a linear velocity distribution in the film, derive an expression for the terminal (zero-acceleration) speed, $V$, of the block. Find the terminal speed of the block if the block mass is $6 \mathrm{~kg}, A=35 \mathrm{~cm}^{2}, \theta=15^{\circ},$ and the film is 1 -mm-thick SAE 30 oil at $20^{\circ} \mathrm{C}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 77

If the velocity distribution in a pipe of radius $R$ is given by
$$
V(r)=V_{0}\left(1-\frac{r^{2}}{R^{2}}\right)
$$
where $V_{0}$ is the velocity at the pipe centerline and $r$ is the distance from the center of the pipe, find (a) the shear stress as a function of $r$ and (b) the shear force on the pipe boundary per unit length of pipe.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 78

Consider the flow of a fluid with viscosity $\mu$ through a circular pipe. The velocity profile in the pipe is shown in Figure 1.31 and is given as $u(r)=u_{\max }\left(1-r^{n} / R^{n}\right)$, where $u_{\max }$ is the maximum flow velocity (which occurs at the centerline), $r$ is the radial distance from the centerline, and $u(r)$ is the flow velocity at any position $r$. Develop an expression for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of pipe.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 79

The velocity distribution, $u(r),$ and the volume flow rate, $Q,$ of a fluid through a pipe are given by
$$
u(r)=\frac{\Delta p}{16 \mu L}\left(D^{2}-4 r^{2}\right), \quad Q=\frac{\pi}{128 \Delta p} \mu L D^{4}
$$
where $r$ is the radial distance from the center of the pipe, $\Delta p$ is the pressure drop over a distance $L$ along the pipe, $\mu$ is the dynamic viscosity of the fluid, and $D$ is the diameter of the pipe. Consider a pipe of diameter $1 \mathrm{~cm}$ that is designed to transport SAE 10 oil. If the volume flow rate is maintained at a fixed value, what would be the percentage difference in pressure drop per unit length of pipe if SAE 30 oil was used instead of SAE 10 oil? What would be the percentage change in shear stress per unit length?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 80

(a) Use Andrade's equation to estimate the viscosity of water at standard atmospheric pressure for temperatures in the range of $0-100^{\circ} \mathrm{C}$ and compare these estimates with the tabulated values given in Appendix B.1. What is the maximum percentage difference between the estimated and tabulated viscosities within this temperature range? (b) Repeat part (a) using the alternative empirical expression given by Equation 1.51 . What equation would you recommend for estimating the viscosity of water in the temperature range of $0-100^{\circ} \mathrm{C} ?$

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 81

The dynamic viscosity of pure nitrogen is estimated to be $16.40 \mu \mathrm{Pa} \cdot \mathrm{s}$ at $0{ }^{\circ} \mathrm{C}$ and $20.94 \mu \mathrm{Pa} \cdot \mathrm{s}$ at $100^{\circ} \mathrm{C}$. Use these data to estimate the dynamic viscosity at $50^{\circ} \mathrm{C}$ using (a) linear interpolation, (b) the Sutherland equation, and (c) the power-law relationship. (d) From the tabulated value of the dynamic viscosity of nitrogen at $50^{\circ} \mathrm{C}$ given in Appendix $\mathrm{B} .6$, identify which of the estimation methods used in parts a-c yields the most accurate estimate of the dynamic viscosity at $50^{\circ} \mathrm{C}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 82

Would you expect that the surface tension of water in contact with air is the same as the surface tension of water in contact with pure oxygen? Explain.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 83

A steel pin is supported on a water surface as shown in Figure $1.32 .$ Find the relationship between the deflection angle, $\theta,$ and the weight of the pin. If the maximum deflection angle that can be sustained is $10^{\circ},$ what is the maximum pin size (i.e., diameter, length) that can be supported by the water?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 84

Solid spheres of varying sizes can be supported to varying extents on the surface of a liquid, depending on the weight and size of the sphere and the surface tension of the liquid. Consider the case where the liquid is water at $20^{\circ} \mathrm{C}$. (a) What diameter lead sphere can be supported on the surface of the water? (b) What diameter concrete sphere can be supported?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 85

Raindrops generally vary in size from $0.5-4 \mathrm{~mm}$. Determine the corresponding range of increased pressure of water within a raindrop compared with the (atmospheric) pressure outside the raindrop. Assume that the temperature of the water in a raindrop is $20^{\circ} \mathrm{C}$

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 86

Using a spray nozzle, small droplets of glycerin are formed in the atmosphere. The droplets have a diameter of $0.6 \mathrm{~mm}$, and the temperature of glycerin is $20^{\circ} \mathrm{C}$. If atmospheric pressure is taken as $101.3 \mathrm{kPa}$, what is the absolute pressure within the droplets?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 87

The free-body diagram of a half-droplet of radius $R$ is shown in Figure $1.33 .$ In this case, $p_{1}$ is the pressure at the center of the droplet, $p_{2}$ is the pressure outside the droplet, $\sigma$ is the surface tension at the liquid-air interface, and $\mathbf{W}$ is the weight of the liquid in the half-droplet. (a) Show that the pressure difference $p_{1}-p_{2}$ is given by
$$
p_{1}-p_{2}=\frac{2 \sigma}{R}-\frac{2}{3} \gamma R
$$
where $\gamma$ is the specific weight of the liquid. Contrast this result with the conventional pressure-difference equation for liquid droplets in air. (b) A manufacturing process utilizes 1.5 -mm-diameter droplets of $\operatorname{SAE} 30$ oil at $20^{\circ} \mathrm{C}$ in air. Contrast the pressure difference between the air and the center of the droplet calculated using the conventional equation with that calculated using Equation $1.67 .$ Assess whether neglecting the weight of the liquid is justified in this case.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 88

A liquid with a surface tension of $0.072 \mathrm{~N} / \mathrm{m}$ is used to form 60 -mm-diameter bubbles in air. What is the difference between the air pressure inside the bubble and the air pressure outside the bubble?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 89

A clean glass capillary tube is placed in pure water. What is the smallest diameter of the capillary tube that can be used such that the capillary rise will be no more than $6 \mathrm{~mm} ?$

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 90

A 1.5-mm-diameter capillary tube is inserted in a liquid, and it is observed that the liquid rises $15 \mathrm{~mm}$ in the tube and has a contact angle of $15^{\circ}$ with the surface of the glass tube. If a hydrometer indicates that the liquid has a specific gravity of $0.8,$ what is the surface tension of the liquid? Would you expect that this same surface tension would be found if the experiment was done using a tube material other than glass? Explain.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 91

A 1 -mm-diameter glass capillary tube is inserted in a beaker of mercury at $20^{\circ} \mathrm{C}$. Previous experimenters report that the contact angle between mercury and the glass material is $127^{\circ} .$ What is the expected depth of depression of mercury in the capillary tube?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 92

Determine the maximum diameter of a glass capillary tube that can be used to cause a capillary rise of benzene that exceeds four tube diameters. Assume a temperature of $25^{\circ} \mathrm{C}$ and assume that the contact angle of benzene on glass is approximately $15^{\circ}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 93

Derive an expression for the capillary rise height $h$ for a liquid of surface tension $\sigma$ and contact angle $\theta$ between two vertical parallel plates a distance $W$ apart as shown in Figure 1.34 . What will $h$ be for water at $20^{\circ} \mathrm{C}$ if $W=0.5 \mathrm{~mm} ?$

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 94

The pressure, $p,$ in a liquid just below the meniscus in a capillary tube with a rise height, $h,$ can be estimated by the hydrostatic pressure relation
$$
p=p_{0}-\gamma h
$$
where $p_{0}$ is the pressure at the liquid surface in the source reservoir and $\gamma$ is the specific weight of the liquid. Consider a capillary tube that is inserted in a reservoir of water at $20^{\circ} \mathrm{C},$ where the water surface in the reservoir is exposed to an atmospheric pressure of $101.3 \mathrm{kPa}$. The surface tension of the water is $73 \mathrm{mN} / \mathrm{m},$ and the contact angle of the water with the capillary-tube material is $5^{\circ} .$ Given that the smallest workable diameter of the capillary tube is the diameter that would cause vaporization (i.e., cavitation) of the water at the meniscus of the liquid in the capillary tube, what is the limiting diameter of the capillary tube?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 95

The difference in pressure across the meniscus of a liquid in a capillary tube can be estimated by the relation
$$
p_{0}-p=\frac{2 \sigma}{R}
$$
where $p_{0}$ is the pressure above the meniscus (usually atmospheric pressure), $p$ is the pressure below the meniscus, $\sigma$ is the surface tension of the liquid, and $R$ is the radius of curvature of the meniscus. (a) Combine Equations 1.68 and 1.69 to determine the relationship between the curvature of the meniscus and the rise height in a capillary tube. (b) If water at $10^{\circ} \mathrm{C}$ has a rise height of $75 \mathrm{~mm}$ in a capillary tube, what is the estimated radius of curvature of the meniscus?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 96

A storage tank is partially filled with gasoline at $20^{\circ} \mathrm{C}$. If the air above the gasoline is pumped out using a vacuum pump, what is the minimum absolute pressure that can be attained in the open space above the gasoline?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 97

(a) If air at $25^{\circ} \mathrm{C}$ is $25 \%$ oxygen and $75 \%$ nitrogen and atmospheric pressure is $101.3 \mathrm{kPa}$, estimate the density of air at $25^{\circ} \mathrm{C}$. (b) If the air described in part (a) is compressed into a $1.5-\mathrm{m}^{3}$ tank with an absolute pressure of $210 \mathrm{kPa}$ and temperature of $20^{\circ} \mathrm{C},$ what is the weight of the air in the tank? (c) If the relative humidity of air is measured as $85 \%$ at $25^{\circ} \mathrm{C}$, estimate the vapor pressure of water and the temperature at which water condensation will begin to occur.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 98

The outside temperature and humidity in the morning are given as $25.6^{\circ} \mathrm{C}$ and $75 \%$ respectively. If the moisture content of the air remains the same throughout the day, estimate the humidity at noon when the temperature is $32.2^{\circ} \mathrm{C}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 99

The temperature and humidity of outside air are $25^{\circ} \mathrm{C}$ and $80 \%,$ respectively, and the interior of a building is cooled such that condensation forms on the glass windows. Estimate the temperature inside the building.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 100

What would be the boiling point of water in a high mountain area where the atmospheric pressure is $90 \mathrm{kPa}$ ?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 101

Water at $50^{\circ} \mathrm{C}$ is poured into an open steel tank where the air above the water surface is at an atmospheric pressure of $101.3 \mathrm{kPa}$. The tank is sealed, and the air in the tank is evacuated with a vacuum pump. A pressure gauge installed in the tank measures the air pressure in the tank relative to atmospheric pressure. What is the gauge reading when the water in the tank begins to boil?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 102

The pressure of water adjacent to any given location on a rotating propeller is inversely proportional to the speed of the propeller at that location. (a) Explain why cavitation adjacent to a propeller is more likely to occur near the tips of the propeller rather than near the hub of the propeller. (b) A study of a particular propeller indicates that the pressure near the tip of the propeller under operational conditions will be around $5 \mathrm{kPa}$ when the temperature of the water is $20^{\circ} \mathrm{C}$. Is cavitation likely to occur? Explain.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 103

A group of nomads in a mountainous terrain do not want to settle at any location where the boiling point of water is less than $92^{\circ} \mathrm{C}$. What is the highest elevation at which they should consider settling?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 104

What minimum allowable pressure will prevent cavitation of water in a pipeline system that transmits water at $35^{\circ} \mathrm{C} ?$ How is this minimum pressure requirement different from that in a pipeline containing gasoline at $20^{\circ} \mathrm{C} ?$

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 105

A pressure gauge on the suction side of a large cooling tower water pump shows an absolute pressure of $7 \mathrm{kPa}$ when the pump is operating under normal conditions. What is the maximum allowable temperature of the water entering the pump that will prevent the occurrence of cavitation?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 106

An underground storage tank is initially completely filled with gasoline at $20^{\circ} \mathrm{C}$ and sealed. If gasoline is withdrawn from the sealed tank (to fill up a car) and a space is created in the tank above the surface of the gasoline, what is the pressure in the space? What types of molecules are contained in the space?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 107

A peanut farmer in south Georgia has drilled a well and found water $12 \mathrm{~m}$ below the ground. To use the water for irrigation, the farmer extends a pipe down the well and connects the pipe to the intake of a pump located on the ground surface. The temperature of the water in the well is $25^{\circ} \mathrm{C}$. It is known from engineering analysis that the gauge pressure, $p,$ at a height $z$ above the water surface is given by
$$
p=-\gamma\left(1+0.24 \frac{Q^{2}}{g D^{5}}\right) z
$$
where $\gamma$ is the specific weight of the water, $Q$ is the volume flow rate, and $D$ is the diameter of the pipe. If atmospheric pressure is $101 \mathrm{kPa}, Q$ is $50 \mathrm{~L} / \mathrm{min},$ and $D$ is $50 \mathrm{~mm}$, determine the height $z$ above the water surface where the water will begin to vaporize (i.e. cavitate). Based on your result, will the farmer's irrigation system work? Explain.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 108

Model tests on a supercavitating torpedo in seawater at $20^{\circ} \mathrm{C}$ indicate that the minimum pressure, $p_{\min }$, on the surface of the torpedo is related to the speed, $V$, of the torpedo by the relation
$$
p_{\min }=120-0.402 V^{2}
$$
where $p_{\min }$ is in $\mathrm{kPa}$ and $V$ is in $\mathrm{m} / \mathrm{s}$. What is the minimum torpedo speed required for cavitation to begin on the surface of the torpedo?

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 109

Estimate the evaporation rate of water that results from a net solar radiation of 20 $\mathrm{MJ} /\left(\mathrm{m}^{2} \cdot \mathrm{d}\right)$. Assume that the temperature of the water body is $20^{\circ} \mathrm{C}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 110

If water in a lake evaporates at a rate of $4.06 \mathrm{~mm} / \mathrm{d}$ without any change in temperature, estimate the net incident radiation. The lake temperature is $15^{\circ} \mathrm{C}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator

Problem 111

Thunderstorms occur when water in the atmosphere condenses in a cloud to form raindrops. Estimate the rate at which energy is supplied to a thunderstorm when water condenses at the rate of $10 \mathrm{~kg} / \mathrm{s}$. The air temperature in the cloud is $5^{\circ} \mathrm{C}$.

Kudakwashe Mapiki

Kudakwashe Mapiki

Numerade Educator