19. Fluid Mechanics

(III) A steel cable is to support an elevator whose total (loaded) mass is not to exceed 3100 kg. If the maximum acceleration of the elevator is 1.8 m/s² , calculate the diameter of cable required. Assume a safety factor of 8.0.

(II) An iron bolt is used to connect two iron plates together. The bolt must withstand shear forces up to about 3600 N. Calculate the minimum diameter for the bolt, based on a safety factor of 7.0.

(II) At depths of 2000 m in the sea, the pressure is about 200 times atmospheric pressure (1 atm = 1.0 x 10⁵ N/m²). By what percentage does the interior space of an iron bathysphere’s volume change at this depth?

(II) (a) What is the maximum tension possible in a 1.00-mm-diameter nylon tennis racket string?

(II) What is the maximum tension possible in a 1.00-mm-diameter nylon tennis racket string? (b) If you want tighter strings, what do you do to prevent breakage: use thinner or thicker strings? Why? What causes strings to break when they are hit by the ball?

(I) What is the difference in blood pressure (mm-Hg) between the top of the head and bottom of the feet of a 1.75-m-tall person standing vertically?

(II) While exploring a sunken ocean liner, a small robot submarine measured the absolute pressure at the level of the ship to be 413 atmospheres.

(b) Calculate the magnitude of the force due to the water on a viewing port of the submarine at this depth if the viewing port has a surface area of 0.0100 m² .

(III) Water stands at a height h behind a vertical dam of uniform width b.

(a) Use integration to show that the total force of the water on the dam is F = 1/2 ρgh²b .

(II) Assume the supports of the uniform cantilever shown in Fig. 12–79 (m = 2900 kg) are made of wood. Calculate the minimum cross-sectional area required of each, assuming a safety factor of 9.0.

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(II) How high would the level be in an alcohol barometer at normal atmospheric pressure?

(III) A beaker of liquid accelerates from rest, on a horizontal surface, with acceleration α to the right.

(c) How does the pressure vary with depth below the surface?

Intravenous transfusions are often made under gravity, as shown in Fig. 13–59. Assuming the fluid has a density of 1.00 g/cm³, at what height h should the bottle be placed so the liquid pressure is

(a) 52 mm-Hg

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Intravenous transfusions are often made under gravity, as shown in Fig. 13–59. Assuming the fluid has a density of 1.00 g/cm³ (c) If the blood pressure is 75 mm-Hg above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein?

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A bicycle pump is used to inflate a tire. The initial tire (gauge) pressure is 210 kPa (30 psi). At the end of the pumping process, the final pressure is 310 kPa (45 psi). If the diameter of the plunger in the cylinder of the pump is 2.5 cm, what is the range of the force that needs to be applied to the pump handle from beginning to end?

Estimate the total mass of the Earth’s atmosphere, using the known value of atmospheric pressure at sea level.