Chapter 9 Test -- Fluid Dynamics

*FREE RESPONSE* A rooftop water storage tower is filled with freshwater to a depth of 6.4m. *(a)* What is the pressure 4.5m below the surface of the water? (b) Use your knowledge of pressure and fluids at rest to explain why the circular metal bands are more closely spaced near the base of the tank.

(a) P = Po + pgh P = (1.013 x 10^5) + 1000 x 4.5 x 9.8 P = 1.454 x 10^5 Pa (subtracted 4.5 from 6.4 for some reason) (b) As depth increases, pressure increases. The metal bands are closer near the bottom because that is where the most pressure, which is pushing out against the tower, exists.

*FREE RESPONSE* A hydraulic lift in the picture above can lift a 12,200N car when a force of 715N is applied to the small piston. If the radius of the large piston is 19cm, what is the radius of the small piston?

F1/A1 = F2/A2 715/A1 = 12,200/(π x 0.19^2) 0.1134 x 715 = 12,200 x A1 81.089 = 12,200 x A1 A1 = 0.0066m^2 A = π x r^2 0.0066 = π x r^2 0.00212 = r^2 r = 0.046m = 4.6cm (didn't read the question fully, solved for area)

FREE RESPONSE Calculate the buoyant force of an air mattress that is 2.3m long, 0.66m wide, and 14cm deep. If the air mattress itself has a mass of 0.22kg, what is the maximum mass it can support in freshwater? (*Hint - let the buoyant force support the air mattress plus the additional mass). Remember, freshwater has a density of 1000kg/m^3

Fb = pVg V = 2.3 x 0.66 x 0.14 = 0.21252 p = 0.22/0.21252 = 1.035 Fb = 1.035 x 0.21252 x 9.8 Fb = 2.156N max density = (m1 + m2)/V max density = 1000 1000 = (0.22 + m2)/0.21252 0.22 + m2 = 212.52 m2 = 212.3kg

*FREE RESPONSE* It's hot! You just finished helping out a friend move into their new house and landscape their front yard. With all of the heavy lifting, digging, and mulching you're thirsty. You see a hose lying on the ground that has water coming out of it at a speed of 5.4m/s. You lift the nozzle of the hose to a height of 1.3m above the ground and you take a drink. At what speed was the water coming out when you took your drink? Let point 1 be on the ground.

P1 + pgy1 + (1/2)(p)(v1)^2 = P2 + pgy2 + (1/2)(p)(v2)^2 ((1000 x 9.8 x 0 + 1/2 x 1000 x 5.4^2 = 1000 x 9.8 x 1.3 + 1/2 x 1000 x v2^2)) 0 + 14580 = 12740 + 500 x v2^2 500 x v2^2 = 1840 v2^2 = 3.68 v2 = 1.918m/s (forgot to take the square root of 3.68)

*FREE RESPONSE* A physics student prepares to blow through a horizontal drinking straw. The air from the horizontal straw will be directed across the top of a vertical straw whose lower end is submerged in a pan of water. When the student blows air through the horizontal straw, does the water level in the vertical straw rise, fall, or stay the same? Briefly explain.

The water level in the vertical straw rises because, as the student blows over the top of the straw, the pressure on top of the straw decreases. Atmospheric pressure is pushing down on the rest of the water in the pan, causing the pressure to attempt to even itself out by forcing the water to migrate towards the lower pressured area of the straw, thus making the water rise. (forgot to mention atmospheric pressure in the original answer)

*MULTIPLE CHOICE* An air bubble underwater has the same pressure as that of the surrounding water. As the air bubble rises toward the surface (and its temperature remains constant), the volume of the air bubble a) increases b) decreases c) remains constant d) increases or decreases, depending on the rate it rises

a) increases Wrong: c (when temperature is constant, volume and pressure are inversely proportionate)

*MULTIPLE CHOICE* Water flows through a pipe. The diameter of the pipe at point B is larger than at point A. Where is the water pressure greatest? a) at point A b) at point B c) it is the same at both A and B d) no pressure exists as both points are the same height

b) at point b Wrong: c (velocity and pressure are inversely proportionate)

MULTIPLE CHOICE When you blow some air above a paper strip, the paper rises. This happens because a) the air above the paper moves faster and the pressure is higher b) the air above the paper moves faster and the pressure is lower c) the air above the paper moves faster and the pressure remains constant d) the air above the paper moves slower and the pressure is higher e) the air above the paper moves slower and the pressure is lower

b) the air above the paper moves faster and the pressure is lower

MULTIPLE CHOICE If a liquid is flowing through a large section of a pipe into a cross-sectional area that is reduced the speed of the fluid will a) remain the same b) slow down as it backs up where the area is reduced c) be increased as the same mass of fluid must pass both points in same amount of time d) it cannot be determined without knowing the volume of the fluid in question

c) be increased as the same mass of fluid must pass both points in same amount of time

*MULTIPLE CHOICE* A piece of wood is floating in a bathtub. A second piece of wood sits on top of the first piece, and does not touch the water. If the top piece is taken off and placed in the water, what happens to the water level in the tub? a) it goes up b) it goes down c) it does not change d) it cannot be determined without the volumes of the two pieces of wood

c) it does not change Wrong: d (unless specifically told otherwise, assume that the pieces of wood are made of the same material)

MULTIPLE CHOICE The water pressure to an apartment is increased by the water company. The water enters the apartment through an entrance valve at the front of the apartment. Where will the increase in the static water pressure be greatest when no water is flowing in the system? a) at a faucet close to the entrance valve b) at a faucet far from the entrance valve c) it will be the same at all faucets d) there will be no increase in the pressure at the faucets

c) it will be the same at all faucets

MULTIPLE CHOICE A cup is filled to the brim with water and a floating ice cube. When the ice melts, the water a) will overflow the cup b) level will decrease to the level equal to the bottom of the ice cube c) level will remain the same since the cube displaced volume equal to its weight d) level will decrease to the level equal to the top of the ice cube

c) level will remain the same since the cube displaced volume equal to its weight

MULTIPLE CHOICE A wooden block contains some nails so that its density is exactly equal to that of water. If it is placed in a tank of water and released from rest when it is completely submerged, it will a) rise to the surface b) sink to the bottom c) remain where it is released d) remain until it equalizes then sink to bottom

c) remain where it is released

*MULTIPLE CHOICE* Consider a brick that is totally immersed in water, with the long edge of the brick vertical. The pressure on the brick is a) the same on all surfaces of the brick b) greatest on the face with largest area c) greatest on the top of the brick d) greatest on the sides of the brick e) greatest on the bottom of the brick

e) greatest on the bottom of the brick Wrong: a (even though it's solid material, there is still more material on top of the bottom of the brick than anywhere is)

MULTIPLE CHOICE As shown in the figure, fluid fills a container having several sections. At which of the indicated points is the pressure greatest? . .|. . . . . .|. . . . . ./. ./. . . .|. .|. . . . . . .\. . . . . . . . . /. . .|~~~~~~|. . . . ./~~/. . . . |~~|. . . . . . . \~~~~~~~~/ . . .|. . . . . .|. . . . /. ./. . . . . |. .|. . . . . . . . \. . . . . ./ . . .|. . A . .|. . . ./B/. . . . . . |C|. . . . . . . . . \. D ./ . . __|............|___ /. ./___________|. .|_______________\. . /______ |___________________________________________________________| a) A b) B c) C d) D e) the pressure is the same at each of the labeled points

e) the pressure is the same at each of the labeled points

*FREE RESPONSE* A horizontal pipe contains water at a pressure of 110kPa flowing with a speed of 1.6m/s. When the pipe narrows to half its original diameter, what is the speed of the water? A = π x r^2

π x r1^2 = π x (1/2 x r1)^2 π x r1^2 = 1/4 x π x r1^2 A2 = 1/4 x A1 A1 x V1 = A2 x V2 A1 x V1 = 1/4 x A1 x V2 (A1 x 1.6)/(1/4 x A1) = V2 1.6 x 4 = V2 V2 = 6.4m/s