Fluid mechanics | Practice Problems, Examples & Solutions

Density

Inorganic Chemistry

LiBr has a density of $3.464 \mathrm{g} / \mathrm{cm}^{3}$ and the NaCl crystal structure. Calculate the interionic distance, and compare your answer with the value from the sum of the ionic radii found in Appendix B-1.

The Crystalline Solid State

0:00

Inorganic Chemistry

Determine the point groups of the following unit cells:
a. Face-centered cubic
b. Body-centered tetragonal
c. $\mathrm{CsCl} \text { (Figure } 7.7)$
d. Diamond (Figure $7.6)$
e. Nickel arsenide (Figure 7.10 )

The Crystalline Solid State

02:44

Chemistry: Introducing Inorganic, Organic and Physical Chemistry

"The density of nitrogen gas in a container at $300 \mathrm{K}$ and 1.0 bar pressure is $1.25 \mathrm{g} \mathrm{dm}^{-3}$ (Section 8.5 ).
(a) Calculate the rms speed of the molecules.
(b) At what the temperature will the ms speed be twice as fast?

Gases

Pressure in a Fluid

132 Practice Problems

02:50

Introduction to General, Organic and Biochemistry

An unknown amount of He gas occupies 30.5 L at 2.00 atm pressure and $300 .$ K. What is the weight of the gas in the container?

Gases, Liquids, and Solids

04:08

21st Century Astronomy

Suppose you seal a rigid container that has been open to air at sea level when the temperature is $0^{\circ} \mathrm{C}(273 \mathrm{K}) .$ The pressure inside the sealed container is now exactly equal to the outside air pressure: $10^{5} \mathrm{N} / \mathrm{m}^{2}$
a. What would be the pressure inside the container if it were left sitting in the desert shade where the surrounding air temperature was $50^{\circ} \mathrm{C}(323 \mathrm{K}) ?$
b. What would be the pressure inside the container if it were left sitting out in an Antarctic night where the surrounding air temperature was $-70^{\circ} \mathrm{C}(203 \mathrm{K}) ?$
c. What would you observe in each case if the walls of the
container were not rigid?

Atmospheres of the Terrestrial Planets

02:40

Fundamentals of Thermodynamics

Are the pressures in the tables absolute or gauge pressures?

Properties of a Pure Substances

Buoyancy

44 Practice Problems

01:19

University Physics

In the last chapter, free convection was explained as the result of buoyant forces on hot fluids. Explain the upward motion of air in flames based on the ideal gas law.

The Kinetic Theory of Gases

03:28

Physics for Scientists and Engineers

(a) A very powerful vacuum cleaner has a hose $2.86 \mathrm{cm}$ in diameter. With no nozzle on the hose, what is the weight of the heaviest brick that the cleaner can lift? (Fig. P11.10a) (b) What If? A very powerful octopus uses one sucker of diameter $2.86 \mathrm{cm}$ on each of the two shells of a clam in an attempt to pull the shells apart (Fig. P14.10b). Find the greatest force the octopus can exert in salt water $32.3 \mathrm{m}$ deep. Cauliom: Experimental verification can be interesting, but do not drop a brick on your foot. Do not overheat the motor of a vacuum cleaner. Do not get an octopus mad at you.

Fluid Mechanics

02:30

Physics for Scientists and Engineers

The small piston of a hydraulic lift has a cross-scrional area of $3.00 \mathrm{cm}^{2},$ and its large piston has a cross-sectional area of $\left.200 \mathrm{cm}^{2} \text { (Figure } 14.4\right) .$ What force must be applied to the small piston for the lift to raise a load of $15.0 \mathrm{kN} ?$ (In service stations, this force is usually exerted by compressed air.)

Fluid Mechanics

Fluid Flow

65 Practice Problems

01:25

Fundamentals of Thermodynamics

Make a control volume that includes the steam flow around in the main turbine loop in the nuclear propulsion system in Fig. 1.3. Identify mass flows (hot or cold) and energy transfers that enter or leave the C.V.

Some Concepts and Definitions

01:28

Fundamentals of Thermodynamics

Make a control volume around the whole power plant in Fig. 1.2 and with the help of Fig. 1.1 list what flows of mass and energy are in or out and any storage of energy. Make sure you know what is inside and what is outside your chosen C.V.

Some Concepts and Definitions

01:05

Fundamentals of Thermodynamics

Make a control volume (C.V.) around the turbine in the steam power plant in Fig. 1.1 and list the flows of mass and energy that are there.

Some Concepts and Definitions

Bernoulli’s Equation

22 Practice Problems

04:12

Calculus of a Single Variable

Solving a Bernoulli Differential Equation In Exercises $59-66,$ solve the Bernoulli differential equation. The Berchoulli equation is a well-known nonlinear equation of the form
$$
y^{\prime}+P(x) y=Q(x) y^{n}
$$
that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is
$$
y^{1-n} e^{\int(1-n) P(x) d x}=\int(1-n) Q(x) e^{f(1-n) P(x) d x} d x+C
$$
$$
y^{\prime}-y=y^{3}
$$

Differential Equations

First-Order Linear Differential Equations

09:44

Calculus of a Single Variable

Differential Equations

First-Order Linear Differential Equations

02:29

Calculus Volume 2

For the following problems, determine how parameter $a$ affects the solution.
Solve the generic equation $y^{\prime}=a x+y .$ How does varying $a$ change the behavior?

Introduction to Differential Equations

First-order Linear Equations

Viscosity and Turbulence

30 Practice Problems

01:58

General Chemistry: Principles and Modern Applications

Butanol and pentane have approximately the same mass, however, the viscosity (at $20^{\circ} \mathrm{C}$ ) of butanol is $\eta=2.948 \mathrm{cP},$ and the viscosity of pentane is $\eta=0.240 \mathrm{cP.}$ Explain this difference.

Intermolecular Forces: Liquids and Solids

00:51

Introductory Chemistry

What is viscosity? How does it depend on intermolecular forces?

Liquids, Solids, and Intermolecular Forces

04:27

Chemistry 2e

The surface tension and viscosity of water at several different temperatures are given in this table.
$$\begin{array}{|c|c|c|}
\hline \text { Water } & \text { Surtace lens on (mivim) } & \text { Viscostiv (mias) } \\
\hline 0^{\circ} \mathrm{C} & 75.6 & 1.79 \\
\hline 20^{\circ} \mathrm{C} & 72.8 & 1.00 \\
\hline 60^{\circ} \mathrm{C} & 66.2 & 0.47 \\
\hline 100^{\circ} \mathrm{C} & 58.9 & 0.28 \\
\hline
\end{array}$$
(a) As temperature increases, what happens to the surface tension of water? Explain why this occurs, in terms of molecular interactions and the effect of changing temperature.
(b) As temperature increases, what happens to the viscosity of water? Explain why this occurs, in terms of molecular interactions and the effect of changing temperature.

Liquids and Solids

Buoyant Forces and Archimedes Principle

19 Practice Problems

01:58

Essential University Physics

Archimedes purportedly used his principle to verify that the king's crown was pure gold by weighing the crown submerged in water. Suppose the crown's actual weight was $25.0 \mathrm{N}$. What would be its apparent weight if it were made of (a) pure gold and (b) $75 \%$ gold and $25 \%$ silver, by volume? The densities of gold, silver, and water are $19.3 \mathrm{g} / \mathrm{cm}^{3}, 10.5 \mathrm{g} / \mathrm{cm}^{3},$ and $1.00 \mathrm{g} / \mathrm{cm}^{3},$ respectively.

Fluid Motion

05:45

College Physics

A spherical weather balloon is filled with hydrogen until its radius is 3.00 $\mathrm{m}$ . Its total mass including the instruments it carries is 15.0 $\mathrm{kg}$ . (a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 $\mathrm{kg} / \mathrm{m}^{3}$ . (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? (c) Why does the radius of the balloon tend to increase as it rises to higher altitude?

Fluids and Solids

06:49

College Physics

A 62.0 -kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions 2.00 $\mathrm{m} \times 2.00 \mathrm{m} \times 0.0900 \mathrm{m} .$ The bottom 0.024 $\mathrm{m}$ of the raft is submerged. (a) Draw a force diagram of the system consisting of the survivor and raft. (b) Write Newton's second law for the system in one dimension, using $B$ for buoyancy, w for the weight of the survivor, and $w_{r}$ for the weight of the raft. (Set $a=0 . )$ (c) Calculate the numeric value for the buoyancy, $B$ . (Seawater has density 1025 $\mathrm{kg} / \mathrm{m}^{3} .$ ) (d) Using the value of $B$ and the weight $w$ of the survivor, calculate the weight $w_{r}$ of the Styrofoam. (e) What is the density of the Styrofoam? (f) What is the maximum buoyant force, corresponding to the raft being submerged up to its top surface? (g) What total mass of survivors can the raft support?

Fluids and Solids

Fluid Kinematics

17 Practice Problems

06:25

Fundamentals of Thermodynamics

A small, high-speed turbine operating on compressed air produces a power output of $100 \mathrm{W}$. The inlet state is $400 \mathrm{kPa}, 50^{\circ} \mathrm{C}$, and the exit state is $150 \mathrm{kPa},-30^{\circ} \mathrm{C} .$ Assuming the velocities to be low and the process to be adiabatic, find the required mass flow rate of air through the turbine.

First Law Analysis for a Control Volume

03:33

University Physics Volume 1

The image shows how sandbags placed around a leak outside a river levee can effectively stop the flow of water under the levee. Explain how the small amount of water inside the column of sandbags is able to balance the much larger body of water behind the levee.

Fluid Mechanics

03:12

University Physics Volume 1

Why is a force exerted by a static fluid on a surface always perpendicular to the surface?

Fluid Mechanics

Fluid Dynamics

35 Practice Problems

07:27

Fundamentals of Thermodynamics

The front of a jet engine acts as a diffuser, receiving air at $900 \mathrm{km} / \mathrm{h},-5^{\circ} \mathrm{C},$ and $50 \mathrm{kPa}$, bringing it to $80 \mathrm{m} / \mathrm{s}$ relative to the engine before entering the compressor (see Fig. $\mathrm{P} 6.39$). If the flow area is reduced to $80 \%$ of the inlet area, find the temperature and pressure in the compressor inlet.

First Law Analysis for a Control Volume

04:52

Fundamentals of Thermodynamics

Air flows into a diffuser at $300 \mathrm{m} / \mathrm{s}, 300 \mathrm{K},$ and $100 \mathrm{kPa} .$ At the exit the velocity is very small but the pressure is high. Find the exit temperature assuming zero heat transfer.

First Law Analysis for a Control Volume

00:24

Fundamentals of Thermodynamics

If you compress air the temperature goes up. Why? When the hot air, high $P$, flows in long pipes, it eventually cools to ambient $T .$ How does that change the flow?

First Law Analysis for a Control Volume