19. Fluid Mechanics

You are designing a diving bell to withstand the pressure of seawater at a depth of 250 m. What is the gauge pressure at this depth? (You can ignore changes in the density of the water with depth.) At this depth, what is the net force due to the water outside and the air inside the bell on a circular glass window 30.0 cm in diameter if the pressure inside the diving bell equals the pressure at the surface of the water? (Ignore the small variation of pressure over the surface of the window.)

You are designing a diving bell to withstand the pressure of seawater at a depth of 250 m. (a) What is the gauge pressure at this depth? (You can ignore changes in the density of the water with depth.)

In intravenous feeding, a needle is inserted in a vein in the patient's arm and a tube leads from the needle to a reservoir of fluid (density 1050 kg/m³) located at height h above the arm. The top of the reservoir is open to the air. If the gauge pressure inside the vein is 5980 Pa, what is the minimum value of h that allows fluid to enter the vein? Assume the needle diameter is large enough that you can ignore the viscosity of the liquid.

A friend asks you how much pressure is in your car tires. You know that the tire manufacturer recommends 30 psi, but it's been a while since you've checked. You can't find a tire gauge in the car, but you do find the owner's manual and a ruler. Fortunately, you've just finished taking physics, so you tell your friend, 'I don't know, but I can figure it out.' From the owner's manual you find that the car's mass is 1500 kg. It seems reasonable to assume that each tire supports one-fourth of the weight. With the ruler you find that the tires are 15 cm wide and the flattened segment of the tire in contact with the road is 13 cm long. What answer—in psi—will you give your friend?

It's possible to use the ideal-gas law to show that the density of the earth's atmosphere decreases exponentially with height. That is, ρ = ρ₀ exp (-z/z₀), where z is the height above sea level, ρ₀ is the density at sea level (you can use the Table 14.1 value), and z₀ is called the scale height of the atmosphere. What is the density of the air in Denver, at an elevation of 1600 m? What percent of sea-level density is this?

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.

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?

An aquarium of length L, width (front to back) W, and depth D is filled to the top with liquid of density ρ. Find an expression for the force of the liquid on the front window of the aquarium.

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?

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?

The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. What is the pressure at point 1?

The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. What is the pressure difference between points 1 and 2? Between points 1 and 3?

(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?

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.