19. Fluid Mechanics

Intro to Pressure

Open Question
The 1.0-m-tall cylinder shown in FIGURE CP14.71 contains air at a pressure of 1 atm. A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. What is the height h of the column of compressed air?
Hint: Boyle's law, which you learned in chemistry, says p₁V₁ = p₂V₂ for a gas compressed at constant temperature, which we will assume to be the case.
Open Question
What is the minimum hose diameter of an ideal vacuum cleaner that could lift a 10 kg (22 lb) dog off the floor?
Open Question
Glycerin is poured into an open U-shaped tube until the height in both sides is 20 cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 20 cm. The two liquids do not mix. What is the difference in height between the top surface of the glycerin and the top surface of the alcohol?
Open Question
An aquarium of length L , width (front to back) W , and depth D is filled to the top with liquid of density p . (b) Find an expression for the force of the liquid on the front window of the aquarium.
Open Question
The deepest point in the ocean is 11 km below sea level, deeper than Mt. Everest is tall. What is the pressure in atmospheres at this depth?
Open Question
A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?
Open Question
The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left.a. What is the pressure at point 1?
Open Question
The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left.b. What is the pressure difference between points 1 and 2? Between points 1 and 3?
Open Question
(II) What is the lift (in newtons) due to Bernoulli’s principle on a wing of area 82 m² if the air passes over the top and bottom surfaces at speeds of 280 m/s and 150 m/s , respectively?
Open Question
During each heartbeat, approximately 70 cm³ of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.
Open Question
(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.
Open Question
(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.
Open Question
(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?
Open Question
(II) (a) What is the maximum tension possible in a 1.00-mm-diameter nylon tennis racket string?
Open Question
(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?