Fluids

Fig. 1 Fig. 2

P1. Water and then oil (which don't mix) are poured into a U-shaped tube, open at both

ends. They come to equilibrium as shown in Fig.1. What is the density of the oil?

Ans. 2

2A+>/< A+>/<

936

3

P2. A hydraulic press for compacting powderered samples has a large cylinder which is

10.0 cm in diameter, and a small cylinder with a diameter of 2.0 cm. A force of 300 N is

applied to the small cylinder. The sample, which is placed on the large cylinder, has an

area of 4.0 cm . What is the pressure on the sample?#

dD

Fin

Ans. "Þ)(& ‚ "!( Nm

P3.* A cylindrical bucket of liquid density is rotated about its symmetry axis, whicha b3is vertical. If the angular velocity is , show that the pressure at a distance r from the=rotation axis is

T œ T <9"

## #3=

where is the pressure at .T < œ !9

P4. A spherically shaped balloon has a radius of 7.35 m, and is filled with helium

(Fig.2). How large a cargo can it lift, assuming that the skin and structure of the balloon

have a mass of 1000 kg? Neglect the buoyant force on the cargo volume itself.

3 3L/ A+>/<$ $œ !Þ"()( œ "Þ# )&!kg/m kg/m kgAns.

P5. A barrel contains a 0.120-m-layer of oil floating on water that is 0.250 ma b] J"%Þ*

deep. The density of the oil is 600 kg/m$

a b+ What is the gauge pressure at the oil-water surface 706 PaAns.

a b, What is the gauge pressure at the bottom of the barrel? 3160 PaAns.

P6. A slab of ice floats on a freshwater lake. What minimum volume musta b] J"%Þ#"

the slab have for a 45.0 kg woman to be able to stand on it without getting her feet wet?

Ans. 0.562 m$

P7. A cubical block of wood, 10.0 cm on a side, floats at the interfacea b] J"%Þ#&

between oil and water with its lower surface 1.50 cm below the interface, as shown on the

diagram. If cm, cm, and the density of the oil is 790 kg/mL œ #! 2 œ "! $

a b+ what is the gauge pressure at the upper face of the block? 116 PaAns.

a b, what is the gauge pressure at the lower face of the block? 921 PaAns.

a b- what is the mass and density of the block? 0.822 kg, 0.822 kg/mAns.$

w ood

water

oil

H

h

P8. A shower head has 20 circular openings, each with radius 1.0 mm. Thea b] J"%Þ#*

shower head is connected to a pipe with raius 0.80 cm. If the speed of water in the pipe is

3.0 m/s, what is its speed as it exits the shower-head openings? m/sAns. 9.6

P9. A sealed tank containing seawater to a height of 11.0 m also contains aira b] J"%Þ$$

above the water at a gauge pressure of 3.00 atm. Water flows out from the bottom

through a small hole. Calculate the speed of the water with which it flows out.

Ans. 28.4 m/s

P10. The deepest point known in any of the earth's oceans is in the Marianasa b] J"%Þ%$

Trench, 10.92 km deep.Assuming water to be incompressible, what is the pressure at this

depth? Use density of seawater 1.10 PaAns. ‚ "!)

P11. How fast does water flow from a hole at the bottom of a very wide, 4.6-m -deep

storage tank filled with water? Ignore viscosity. 9.5 m/sAns.

P12. What is the lift (in newtons) due to Bernoulli's principle on a wing of area 86 m if#

the air passes over the top and bottom surfaces at speeds of 340 m/s and 290 m/s,

respectively. NAns. "Þ' ‚ "!'