Chapter 9 Solutions — Mechanical Properties of Fluids

Exercises

1. 1.
   Explain why

   • (a) The blood pressure in humans is greater at the feet than at the brain
   • (b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km
   • (c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.
2. 2.
   Explain why

   • (a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
   • (b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops.
   • (c) Surface tension of a liquid is independent of the area of the surface.
   • (d) Water with detergent dissolved in it should have small angles of contact.
   • (e) A drop of liquid…
3. 3.
   Fill in the blanks using the word(s) from the list appended with each statement:

   • (a) Surface tension of liquids generally . . . with temperatures (increases / decreases)
   • (b) Viscosity of gases . . . with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)
   • (c) For solids with elastic modulus of rigidity, the shearing force is proportional to . . . , while for…
4. 4.
   Explain why

   • (a) To keep a piece of paper horizontal, you should blow over, not under, it
   • (b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers
   • (c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
   • (d) A fluid flowing out of a small hole in a…
5. 5.
   A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor?
6. 6.
   Torricelli's barometer used mercury. Pascal duplicated it using French wine of density 984 kg m⁻³. Determine the height of the wine column for normal atmospheric pressure.
7. 7.
   A vertical off-shore structure is built to withstand a maximum stress of 10⁹ Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.
8. 8.
   A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is 425 cm². What maximum pressure would the smaller piston have to bear?
9. 9.
   A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit?
10. 10.
    In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)
11. 11.
    Can Bernoulli's equation be used to describe the flow of water through a rapid in a river? Explain.
12. 12.
    Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli's equation? Explain.
13. 13.
    Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 × 10⁻³ kg s⁻¹, what is the pressure difference between the two ends of the tube? (Density of glycerine = 1.3 × 10³ kg m⁻³ and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is…
14. 14.
    In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 70 m s⁻¹ and 63 m s⁻¹ respectively. What is the lift on the wing if its area is 2.5 m²? Take the density of air to be 1.3 kg m⁻³.
15. 15.
    Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect? Why?
16. 16.
    The cylindrical tube of a spray pump has a cross-section of 8.0 cm², one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min⁻¹, what is the speed of ejection of the liquid through the holes?
17. 17.
    A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10⁻² N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?
18. 18.
    Figure 9.21(a) shows a thin liquid film supporting a small weight = 4.5 × 10⁻² N. What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c)? Explain your answer physically.
19. 19.
    What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature? Surface tension of mercury at that temperature (20 °C) is 4.65 × 10⁻¹ N m⁻¹. The atmospheric pressure is 1.01 × 10⁵ Pa. Also give the excess pressure inside the drop.
20. 20.
    What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 °C) is 2.50 × 10⁻² N m⁻¹? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is…