8.1.3 How Pressure Varies with Depth

Question 1

How Pressure Varies with Depth

Answer 1

• By applying Newton’s second law you can derive the relationship between pressure and depth within an incompressible fluid.
• For two points and separated by a height h within an incompressible fluid, the difference in pressure is given by, where r is the fluid’s density and g is the free-fall acceleration.
• In devices that measure pressure (P), the gauge pressure is, where is the atmospheric pressure

Question 2

Consider the diagram of the apparatus where the liquid in the A side is water, and the liquid in the B side is mercury. The two liquids are at the same height and are separated by the partition as shown. The density of mercury is 13.6 g / cm3. When the partition is removed, the boundary between the liquids will ______________.

Answer 2

move to the left

Question 3

Consider a 15 cm square drain cover that is at a depth of 4 m below the surface of water. Assume that the water is at rest and open to the atmosphere. Use the average atmospheric pressure at sea level, which 1.01 × 105 N / m2. What is the total force on the cover?

Answer 3

3.15 × 10^3 N

Question 4

Evaluate the following as true or false. A variety of instruments measure the pressure of a fluid. The measurement is called the gauge pressure. In the formula P = P0 + pgh, P is the absolute pressure, pgh is the gauge pressure, and p0 is the atmospheric pressure. Therefore, Pg = p - P0. An example is a tire gauge. If is reads 30 lb/in^2, or 200 kPa, the actual pressure within the tire is 1 atm higher, or 201 kPa. This applies to open-tube or closed-tube system.

Answer 4

false

Question 5

Which of the following statements concerning pressure is not correct?

Answer 5

Although derived for a liquid, the formula P2 = P1 + pgh applies to fluids in general

Question 6

We have used the derived formula p2 = p1 + pgh. for the pressure at a point p2 below p1. Which of the following expansions of this equation is not correct?

Answer 6

Because p = m/V, p = (mg/V) x h; therefore, increasing the volume decreases the pressure

Question 7

Consider a person’s eardrum at a depth of 3 meters below the surface of water. Which of the following is the force exerted on the eardrum by the water pressure? Assume that the person’s eardrum is 0.36 cm2 in area.

Answer 7

1.06 N

Question 8

Consider a container that is 0.5 m x 0.5 m x 0.5 m filled with a liquid in hydrostatic equilibrium. Which of the following is incorrect?

Answer 8

The change in pressure between any two heights in a liquid is inversely proportional to the density of the liquid.

Question 9

Consider the three flasks of water, each with the same area at the bottom and each having the same height. If flask A contains a larger volume of water than flask B, and flask B contains a larger volume of water than flask C, which of the following is correct?

Answer 9

The pressure at the base of all three flasks is the same.

Question 10

Consider an imaginary cube within a container of liquid. Which of the following statements concerning pressure and forces in a container of liquid in hydrostatic equilibrium is not correct?

Answer 10

The pressure applied to the cube is perpendicular to a particular surface.