Watering plants You water flowers outside your house. (a) Determine the flow rate of water moving at an average speed of 32 cm/s through a garden hose of radius 1.2 cm. (b) Determine the speed of the water in a second hose of radius 1.0 cm that is connected to the first hose.

Netra S.

University of Wisconsin - Milwaukee

Irrigation canal You live near an irrigation canal that is filled to the top with water. (a) It has a rectangular cross section of 5.0-m width and 1.2-m depth. If water flows at a speed of 0.80 m/s, what is its flow rate? (b) If the width of the stream is reduced to 3.0 m and the depth to 1.0 m as the water passes a

flow-control gate, what is the speed of the water past the gate?

Netra S.

University of Wisconsin - Milwaukee

Fire hose During a fire, a firefighter holds a hose through which 0.070 ${m}^{3}$ of water flows each second. The water leaves the nozzle at an average speed of 25 ${m} / {s}$ . What information about the hose can you determine using these data?

Netra S.

University of Wisconsin - Milwaukee

The main waterline for a neighborhood delivers water at a maximum flow rate of 0.010 ${m}^{3} / {s}$ . If the speed of this water is $0.30 {m} / {s},$ what is the pipe's radius?

Netra S.

University of Wisconsin - Milwaukee

BIO Blood flow in capillaries The flow rate of blood in the aorta is 80 ${cm}^{3} / {s}$ . Beyond the aorta, this blood eventually travels through about $6 \times 10^{9}$ capillaries, each of radius $8.0 \times 10^{-4} {cm} .$ What is the speed of the blood in the capillaries?

Netra S.

University of Wisconsin - Milwaukee

Irrigating a field It takes a farmer 2.0 h to irrigate a field using a 4.0-cm-diameter pipe that comes from an irrigation canal. How long would the job take if he used a 6.0-cm pipe? What assumption did you make? If this assumption is not correct, how will your answer change?

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Represent the process sketched in Figure P11.7 using a qualitative Bernoulli bar chart and an equation (include only terms that are not zero).

Netra S.

University of Wisconsin - Milwaukee

Represent the process sketched in Figure P11.8 using a qualitative Bernoulli bar chart and an equation (include only terms that are not zero).

Netra S.

University of Wisconsin - Milwaukee

Fluid flow problem Write a symbolic equation (include only terms that are not zero) and draw a sketch of a situation that could be represented by the qualitative Bernoulli bar chart shown in Figure P11.9 (there are many possibilities).

Netra S.

University of Wisconsin - Milwaukee

Repeat Problem 9 using the bar chart in Figure P11.10.

Netra S.

University of Wisconsin - Milwaukee

Repeat Problem 9 using the bar chart in Figure P11.11.

Netra S.

University of Wisconsin - Milwaukee

An application of Bernoulli’s equation is shown below. Construct a qualitative Bernoulli bar chart that is consistent with the equation and draw a sketch of a situation that could be represented by the equation (there are many possibilities). $\rho g y_{2}=0.5 \rho v_{1}^{2}$

Netra S.

University of Wisconsin - Milwaukee

Repeat Problem 13 using the equation below. The size of the symbols represents the relative magnitudes of the physical quantities at two points. $0.5 \rho v_{1}^{2}+\left(P_{1}-P_{2}\right)=$

0.5$\rho v_{2}^{2}$

Netra S.

University of Wisconsin - Milwaukee

Repeat Problem 13 using the equation below. The size of the symbols represents the relative magnitudes of the physical quantities at two points. $0.5 \rho v_{1}^{2}+\left(P_{1}-P_{2}\right)=$

$0.5 \rho v_{2}^{2}+\rho g y_{2}$

Netra S.

University of Wisconsin - Milwaukee

Wine flow from barrel While visiting a winery, you observe wine shooting out of a hole in

the bottom of a barrel. The top of the barrel is open. The hole is 0.80 m below the top surface of the wine. Represent this process in multiple ways (a sketch, a bar chart, and an equation) and apply Bernoulli’s equation to a point at the top surface of the wine and another point at the hole in the barrel.

Netra S.

University of Wisconsin - Milwaukee

Water flow in city water system Water is pumped at high speed from a reservoir into a large-diameter pipe. This pipe connects to a smaller diameter pipe. There is no change in elevation. Represent the water flow from the large pipe to the smaller pipe in multiple ways—a sketch, a bar chart, and an equation.

Netra S.

University of Wisconsin - Milwaukee

The pressure of water flowing through a 0.060-m-radius pipe at a speed of 1.8 ${m} / {s}$ is $2.2 \times 10^{5} {N} / {m}^{2} .$ What is ( a ) the flow rate of the water and (b) the pressure in the water after it

goes up a 5.0-m-high hill and flows in a 0.050-m-radius pipe?

Netra S.

University of Wisconsin - Milwaukee

Siphoning water You want to siphon rainwater and melted snow from the cover of an above-ground swimming pool. The cover is 1.4 m above the ground. You have a plastic hose of 1.0-cm radius with one end in the water on the pool cover and the other end on the ground. (a) At what speed does water

exit the hose? (b) If you want to empty the pool cover in half the time, how much wider should the hose be? (c) How much faster does the water flow through this wider pipe?

Netra S.

University of Wisconsin - Milwaukee

Cleaning skylights You are going to wash the skylights in your kitchen. The skylights are 8.0 m above the ground. You connect two garden hoses together—a 0.80-cm-radius hose to a 1.0-cm-radius hose. The smaller hose is held on the roof of the house and the wider hose is attached to the faucet on the ground. The pressure at the opening of the smaller hose is 1 atm, and you want the water to have the speed of 6.0 m/s. What should be the pressure at ground level in the large hose? What should be the speed?

Netra S.

University of Wisconsin - Milwaukee

Community water system A large city waterline pipe has radius 0.060 m and feeds ten smaller pipes, each of radius 0.020 m, that carry water to homes. The flow rate of water in each of the smaller pipes is to be $6.0 \times 10^{-3} {m}^{3} / {s},$ and the pressure is $4.00 \times 10^{5} {N} / {m}^{2} .$ The homes are 10.0 ${m}$ above the main pipe. What is the average speed of the water in (a) a smaller pipe and (b) the main pipe? (c) What is the pressure in the main pipe?

Netra S.

University of Wisconsin - Milwaukee

BIO Blood flow in artery Blood flows at an average speed of 0.40 m/s in a horizontal artery of radius 1.0 cm. The average pressure is $1.4 \times 10^{4} {N} / {m}^{2}$ above atmospheric pressure (the gauge pressure). (a) What is the average speed of the blood past a constriction where the radius of the opening is 0.30 cm? (b) What is the gauge pressure of the blood as it moves past the constriction?

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Window in wind You are on the 48th floor of the Windom Hotel. The day is stormy, and you wonder whether the hotel is a safe place. According to the weather report, the air speed is 20 m/s; the size of the window in your room is 1.0 m * 2.0 m (a) What is the difference in pressure between the inside and

outside air? (b) What is the net force that the air exerts on the window (magnitude and direction)? (c) What assumption did you make to answer these questions?

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Straw aspirator A straw extends out of a glass of water by a height h. How fast must air blow across the top of the straw to draw water to the top of the straw?

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Gate for irrigation system You observe water at rest behind an irrigation dam. The water is 1.2 m above the bottom of a gate that, when lifted, allows water to flow under the gate. Determine the height h from the bottom of the dam that the gate should be lifted to allow a water flow rate of

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A 5.0 -cm-radius horizontal water pipe is 500 ${m}$ long. Water at $20^{\circ} {C}$ flows at a rate of $1.0 \times 10^{-2} {m}^{3} / {s}$ . (a) Determine the pressure drop due to viscous friction from the beginning to the end of the pipe. (b) What radius pipe must you use if you want to keep the pressure difference constant and double the flow rate?

Netra S.

University of Wisconsin - Milwaukee

Fire hose A volunteer firefighter uses a 5.0-cm-diameter fire hose that is 60 m long. The water moves through the hose at 12 m/s. The temperature outside is $20^{\circ} {C}$. What is the pressure drop due to viscous friction across the hose?

Netra S.

University of Wisconsin - Milwaukee

Another fire hose The pump for a fire hose can develop a maximum pressure of $6.0 \times 10^{5} {N} / {m}^{2} .$ A horizontal hose that is 50 ${m}$ long is to carry water of viscosity $1.0 \times 10^{-3} {N} \cdot {s} / {m}^{2}$ at a flow rate of 1.0 ${m}^{3} / {s}$ . What is the minimum radius for the hose?

Netra S.

University of Wisconsin - Milwaukee

Solar collector water system Water flows in a solar collector through a copper tube of radius R and length l. The average temperature of the water is $T^{\circ} {C}$ and the flow rate is $Q {cm}^{3} / {s}$ . Explain how you would determine the viscous pressure drop along the tube, assuming the water does not change elevation.

Netra S.

University of Wisconsin - Milwaukee

BIO Blood flow through capillaries Your heart pumps blood at a flow rate of about 80 ${cm}^{3} / {s}$ . The blood flows through approximately $9 \times 10^{9}$ capillaries, each of radius $4 \times 10^{-4} {cm}$ and 0.1 ${cm}$ long. Determine the viscous friction pressure drop across a capillary, assuming a blood viscosity of $4 \times 10^{-3} {N} \cdot {s} / {m}^{2}$

Netra S.

University of Wisconsin - Milwaukee

BIO Flutter in blood vessel A person has a $5200-{N} / {m}^{2}$ gauge pressure of blood flowing at 0.50 m/s inside a 1.0-cm- radius main artery. The gauge pressure outside the artery is 3200 ${N} / {m}^{2} .$ When using his stethoscope, a physician hears a fluttering sound farther along the artery. The sound is a

sign that the artery is vibrating open and closed, which indicates that there must be a constriction in the artery that has reduced its radius and subsequently reduced the internal blood pressure to less than the external $3200-{N} / {m}^{2}$ pressure. What is the maximum artery radius at this construction?

Netra S.

University of Wisconsin - Milwaukee

BIO Effect of smoking on arteriole radius The average radius of a smoker’s arterioles, the small vessels carrying blood to the capillaries, is 5% smaller than those of a nonsmoker.

(a) Determine the percent change in flow rate if the pressure across the arterioles remains constant.

(b) Determine the percent change in pressure if the flow rate remains constant.

Netra S.

University of Wisconsin - Milwaukee

Roof of house in wind The mass of the roof of a house is $2.1 \times 10^{4} {kg}$ and the area of the roof is 160 ${m}^{2}$ . At what speed must air move across the roof of the house so that

the roof is lifted off the walls? Indicate any assumptions you made.

Netra S.

University of Wisconsin - Milwaukee

You have a U-shaped tube open at both ends. You pour water into the tube so that it is partially filled. You have a fan that blows air at a speed of 10 m/s. (a) How can you use the fan to make water rise on one side of the tube? Explain your strategy in detail. (b) To what maximum height can you get the water

to rise? Note: You cannot touch the water yourself.

Netra S.

University of Wisconsin - Milwaukee

Determine the ratio of the flow rate through capillary tubes A and ${B}$ (that is, ${Q}_{{A}} / {Q}_{B} ) .$ The length of ${A}$ is twice that of ${B}$ , and the radius of ${A}$ is one-half that of ${B}$ . The pressure across both tubes is the same.

Netra S.

University of Wisconsin - Milwaukee

A piston pushes $20^{\circ} {C}$ water through a horizontal tube of 0.20-cm radius and 3.0-m length. One end of the tube is open and at atmospheric pressure. (a) Determine the force needed to push the piston so that the flow rate is 100 ${cm}^{3} / {s}$ (b) Repeat the problem using SAE 10 oil instead of water.

Netra S.

University of Wisconsin - Milwaukee

Engineers use a venturi meter to measure the speed of a fluid traveling through a pipe (see Figure P11.37). Positions 1 and 2 are in pipes with surface areas $A_{1}$ and $A_{2},$ with $A_{1}$ greater than $A_{2}$ , and are at the same vertical height. How can you determine the relative speeds at positions 1 and 2 and the pressure difference between positions 1 and 2$?$

Netra S.

University of Wisconsin - Milwaukee

How can you use the venturi meter system (see Problem 37) to determine whether viscous fluid needs an additional pressure difference to flow at the same speed as a nonviscous fluid?

Netra S.

University of Wisconsin - Milwaukee

Car drag A $2300-{kg}$ car has a drag coefficient of 0.60 and an effective frontal area of 2.8 ${m}^{2}$ . Determine the air drag force on the car when traveling at (a) 24 ${m} / {s}(55 {mi} / {h})$ and $({b}) 31$

${m} / {s}(70 {mi} / {h})$

Netra S.

University of Wisconsin - Milwaukee

EST Air drag when biking Estimate the drag force opposing your motion when you ride a bicycle at 8 m/s.

Netra S.

University of Wisconsin - Milwaukee

BIO Drag on red blood cell Determine the drag force on a red blood cell with a radius of $1.0 \times 10^{-5} {m}$ and moving through $20^{\circ} {C}$ water at speed $1.0 \times 10^{-5} {m} / {s}$ . (Assume laminar flow.)

Netra S.

University of Wisconsin - Milwaukee

BIO ES T Protein terminal speed A protein of radius $3.0 \times 10^{-9} {m}$ falls through a tube of water with viscosity $\eta=1.0 \times 10^{-3} {N} \cdot {s} / {m}^{2}$ . Earth exerts a constant downward

$3.0 \times 10^{-22}-{N}$ force on the protein. (a) Use Stokes's law and the information provided to estimate the terminal speed of the protein. Assume no buoyant force is exerted on the protein. (b) How many hours would be required for the protein to fall 0.10 m?

Netra S.

University of Wisconsin - Milwaukee

Earth exerts a constant downward force of $7.5 \times 10^{-13}$ N on a clay particle. The particles settle 0.10 ${m}$ in 820 ${min}$ . Determine the radius of a clay particle. Assume no buoyant force is exerted on the clay particle. The viscosity of water is $1.0 \times 10^{-3} {N} \cdot {s} / {m}^{2}$

Netra S.

University of Wisconsin - Milwaukee

A sphere falls through a fluid. Earth exerts a constant down- ward 0.50-N force on the sphere. The fluid exerts an opposing drag force on the fluid given by $F_{{D}}=2 v,$ where $F_{{D}}$ is in newtons if $v$ is in meters per second. Determine the terminal speed of the sphere.

Netra S.

University of Wisconsin - Milwaukee

Terminal speed of balloon A balloon of mass m drifts down through the air. The air exerts a resistive drag force on the balloon described by the equation $F_{{D}}=0.03 {v}^{2}$ where $F_{{D}}$ is in newtons if $v$ is in meters per second. What is the terminal speed of the balloon?

Netra S.

University of Wisconsin - Milwaukee

EST A cooler filled with water has a hole of radius 0.40 cm at the bottom. The hole is originally closed with a plug. The cooler is about 1.0 m tall, and the bottom has area 0.4 m * 0.6 m. Determine the initial flow rate of water after removing the plug. Estimate how long it will take to empty the cooler. What assumptions did you make? If they are not valid, will the real time be greater or smaller than the estimate?

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Design an elevator-like device that can lift you to your dorm room by blowing air across the top surface of the elevator. Be sure to provide the details in your design and indicate any difficulties you might encounter.

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BIO Pressure needed for intravenous needle A glucose solution of viscosity $2.2 \times 10^{-3} {N} \cdot {s} / {m}^{2}$ and density 1030 ${kg} / {m}^{3}$ flows from an elevated open bag into a vein. The needle into the vein has a radius of 0.20 mm and is 3.0 cm long. All other tubes leading to the needle have much larger radii, and viscous forces in them can be ignored. The pressure in the vein is 1000 ${N} / {m}^{2}$ above atmospheric pressure. (a) Determine the pressure relative to atmospheric pressure needed at the entrance of the needle to maintain a flow rate of 0.10 ${cm}^{3} / {s}$. (b) To what elevation should the bag containing the glucose be raised to maintain this pressure at the needle?

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Viscous friction with Bernoulli We can include the effect of viscous friction in Bernoulli’s equation by adding a term for the thermal energy generated by the viscous retarding force exerted on the fluid. Show that the term to be added to Eq. (11.5) for flow in a vessel of uniform cross-sectional area A is

$$\frac{\Delta U_{{Th}}}{V}=\frac{4 \pi \eta l v}{A}$$

where $v$ is the average speed of the fluid of viscosity $\eta$ along the center of a pipe whose length is $l$ .

Netra S.

University of Wisconsin - Milwaukee

(a) Show that the work $W$ done per unit time $\Delta t$ by viscous friction in a fluid with a flow rate $Q$ across which there is a pressure drop $\Delta P$ is

$$\frac{W}{\Delta t}=\Delta P Q=Q^{2} R=\frac{\Delta P^{2}}{R}$$

where $R=8 \eta l / \pi r^{4}$ is called the flow resistance of the fluid moving through a vessel of radius $r$ . (b) By what percentage must the work per unit time increase if the radius of a vessel decreases by 10$\%$ and all other quantities including the flow rate remain constant (the pressure does not remain constant)?

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EST BIO Thermal energy in body due to viscous friction Estimate the thermal energy generated per second in a normal body due to the viscous friction force in blood as it moves through the circulatory system.

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BIO Essential hypertension Suppose your uncle has hypertension that causes the radii of his 40,000 arterioles to decrease by 20%. Each arteriole initially was 0.010 mm in radius and 1.0 cm long. By what factor does the resistance $R=8 \eta l / \pi r^{4}$ to blood flow through an arteriole change because of these decreased radii? The pressure drop across all of the arterioles is about 60 ${mm}$ Hg. If the flow rate remains the same, what now is the pressure drop change across the arteriole part of the circulatory system?

Netra S.

University of Wisconsin - Milwaukee

Parachutist A parachutist weighing 80 kg, including the parachute, falls with the parachute open at a constant 8.5-m/s speed toward Earth. The drag coefficient $C_{{D}}=0.50 .$ What is the area of the parachute?

Netra S.

University of Wisconsin - Milwaukee

A 0.20-m-radius balloon falls at terminal speed 0.40 m/s. If the drag coefficient is 0.50, what is the mass of the balloon?

Netra S.

University of Wisconsin - Milwaukee

Terminal speed of skier A skier going down a slope of angle $\theta$ below the horizontal is opposed by a turbulent drag force that the air exerts on the skier and by a kinetic friction force that the snow exerts on the skier. Show that the terminal speed is

$$v_{{T}}=\left[\frac{2 m g(\sin \theta-\mu \cos \theta)}{C_{{D}} \rho A}\right]^{1 / 2}$$

where $\mu$ is the coefficient of kinetic friction between the skis and the snow, $\rho$ is the density of air, $A$ is the skier's frontal area, and $C_{{D}}$ is the drag coefficient.

Netra S.

University of Wisconsin - Milwaukee

A grain of sand of radius 0.15 ${mm}$ and density 2300 ${kg} / {m}^{3}$ is placed in a $20^{\circ} {C}$ lake. Determine the terminal speed of the sand as it sinks into the lake. Do not forget to include the buoyant force that the water exerts on the grain.

Netra S.

University of Wisconsin - Milwaukee

EST Comet crash On June $30,1908,$ a monstrous comet fragment of mass greater than $10^{9} {kg}$ is thought to have devastated a $2000-{km}^{2}$ area of remote Siberia (this impact was called the Tunguska event). Estimate the terminal speed of such a comet in air of density 0.70 ${kg} / {m}^{3} .$ State all of your assumptions. solution (density 1000 ${kg} / {m}^{3}$ and viscosity $1.0 \times 10^{-3} {N} \cdot {s} / {m}^{2} )$ drains from the open bag down the $0.6-m-lon g, 2.0 \times 10^{-3}-m$ radius tube and then through the $0.020-m-lon g, 4.0 \times 10^{-4}-{m}$ radius needle and into the vein? The gauge pressure in the vein in the arm is $+930 {N} / {m}^{2}$ (or 7 ${mm}$ Hg). The nurse says the flow rate should be $0.20 \times 10^{-6} {m}^{3} / {s}(0.2 {cm}^{3} / {s})$

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Which answer below is closest to the speed with which the glucose should flow out of the end of the needle at position 2 in Figure 11.13b?

(a) 0.0004 m/s

(b) 0.004 m/s

(c) 0.04 m/s

(d) 0.4 m/s

(e) 4 m/s

Netra S.

University of Wisconsin - Milwaukee

Which answer below is closest to the speed with which the glucose should flow through the end of the tube just to the right of position 1 in Figure 11.13b?

(a) 0.0002 m/s

(b) 0.002 m/s

(c) 0.02 m/s

(d) 0.2 m/s

(e) 2 m/s

Netra S.

University of Wisconsin - Milwaukee

Assume that there is no resistive friction pressure drop across the needle (as could be determined using Poiseuille’s law). Use the Bernoulli equation and the results from Problems 58 and 59 to determine which answer below is closest to the change in pressure between positions 1 and 2$\left(P_{1}-P_{2}\right)$ in

Figure 11.13 ${b}$ .

(a) 8 ${N} / {m}^{2}$ (b) 80 ${N} / {m}^{2}$ (c) 800 ${N} / {m}^{2}$

(d) 8000 ${N} / {m}^{2}$ (e) $80,000 {N} / {m}^{2}$

Netra S.

University of Wisconsin - Milwaukee

Now, in addition to the Bernoulli pressure change from position 1 to position 2 calculated in Problem 60, there may be a Poiseuille resistive friction pressure change across the needle from position 1 to position 2. Which answer below is closest to that pressure change?

(a) 0.4 ${N} / {m}^{2}$ (b) 4 ${N} / {m}^{2}$ (c) 40 ${N} / {m}^{2}$

(d) 400 ${N} / {m}^{2}$ (e) 4000 ${N} / {m}^{2}$

Netra S.

University of Wisconsin - Milwaukee

The blood pressure in the vein at position 2 in Figure 11.13 ${b}$ at the exit of the needle into the blood is 930 ${N} / {m}^{2}$ . Use this value and the results of Problems 60 and 61 to determine which answer below is closest to the gauge pressure at position 1 in the tube carrying the glucose to the needle.

(a) 1010 ${N} / {m}^{2}$ (b) 1410 ${N} / {m}^{2}$ (c) 1980 ${N} / {m}^{2}$

(d) 2800 ${N} / {m}^{2}$ (e) 4620 ${N} / {m}^{2}$

Netra S.

University of Wisconsin - Milwaukee

Suppose that there is no Poiseuille resistive friction pressure decrease from the top of the glucose solution in the open bag (position 1 in Figure 11.13a) through the tube and down to position 2 near the entrance to the needle. Which answer below is closest to the minimum height of the top of the bag in

order for the glucose to flow down from the tube and through the needle into the blood? Remember that the pressure at position 1 is atmospheric pressure, which is a zero gauge pressure.

(a) 0.04 m (b) 0.08 m (c) 0.14 m

(d) 0.27 m (e) 0.60 m

Netra S.

University of Wisconsin - Milwaukee

Suppose there is a Poiseuille resistive friction pressure decrease from the top of the glucose solution (position 1 in Figure 11.13a) through the tube and down to position 2 near the entrance to the needle. How will this affect the placement of the bag relative to the arm?

(a) The bag will need to be higher.

(b) The bag can remain the same height above the arm.

(c) The bag can be placed lower relative to the arm

(d) Too little information is provided to answer the question.

Netra S.

University of Wisconsin - Milwaukee

The capillaries typically produce about 25% of the resistance to blood flow. Which pressure drop below is closest to the pressure drop across the group of capillaries?

(a) 5 mm Hg (b) 15 mm Hg (c) 25 mm Hg

(d) 35 mm Hg (e) 45 mm Hg

Netra S.

University of Wisconsin - Milwaukee

We found that the arteriole resistance to fluid flow was about 0.62 ${mm} {Hg} /({cm}^{3} / {s}) .$ By what factor would you expect the resistance of all the arterioles to change if the radius of each arteriole decreased by 0.8$?$

(a) 1.3 (b) 1.6 (c) 2.4 (d) 0.4 (e) 0.6

Netra S.

University of Wisconsin - Milwaukee

Why is the resistance to fluid flow through unobstructed arteries relatively small compared to resistance to fluid flow through the arterioles and capillaries?

(a) The arteries are nearer the heart.

(b) There are a relatively small number of arteries.

(c) The artery radii are relatively large.

(d) b and c

(e) a, b, and c

Netra S.

University of Wisconsin - Milwaukee

The huge number of capillaries and venules is needed to

(a) provide nutrients (such as ${O}_{2} )$ and remove waste products from all of the body cells.

(b) distribute water uniformly throughout the body.

(c) reduce the resistance of the circulatory system.

(d) b and c

(e) a, b, and c

Netra S.

University of Wisconsin - Milwaukee

Which number below best represents the ratio of the resistance of a single capillary to the resistance of a single arteriole, assuming they are equally long?

(a) 40 (b) 6 (c) 2.5 (d) 0.4 (e) 0.026

Netra S.

University of Wisconsin - Milwaukee