Question 1

A hydraulic lift, as shown in the image, uses two pistons with areas $$A_1$$ and $$A_2. If a $$force $$F_1 is $$applied to the smaller piston, what is the force $$F_2$$ exerted by the larger piston, assuming the fluid is incompressible and the system is ideal?

Accepted Answer

$$F_2$$ = $$F_1$$ \frac{$$A_2$$}{$$A_1$$}$$

Question 2

Which principle explains why the pressure applied to a confined fluid is transmitted undiminished throughout the fluid?

Accepted Answer

Pascal's Principle

Question 3

A beaker with a circular base of diameter $$0.10\,\mathrm{m}$$ contains water to a depth of $$0.20\,\mathrm{m}. If $$the density of water is $$1000\,\mathrm{kg/m^3$}$$ and atmospheric pressure is ignored, what is the force exerted by the water on the base? (Use $$g = 9.8\,\mathrm{m/s^2$})$$

Accepted Answer

$$F = 154\,\mathrm{N}$$

Question 4

If the pressure at a certain depth in a fluid is $$P$$, and the area of the base is $$A$$, what is the formula for the force exerted by the fluid on the base?

Accepted Answer

$$F = P \cdot A$$

Question 5

A hydraulic car lift has a small piston with area $$0.01\,\mathrm{m^2$}$$ and a large piston with area $$0.50\,\mathrm{m^2$}. If a $$mechanic applies a force of $$200\,\mathrm{N} to $$the small piston, what is the maximum weight that can be lifted by the large piston (ignoring friction and fluid weight)?

Accepted Answer

$$10,000\,\mathrm{N}$$

Question 6

Which of the following best describes the hydrostatic paradox?

Accepted Answer

The force at the base of containers with the same fluid depth and base area is the same, regardless of the container's shape.

Question 7

A sealed container is filled with oil of density $$900\,\mathrm{kg/m^3$} to a $$depth of $$0.5\,\mathrm{m}. $$What is the pressure at the bottom due to the oil? (Use $$g = 9.8\,\mathrm{m/s^2$})$$

Accepted Answer

$$P = 4,410\,\mathrm{Pa}$$

Question 8

If the area of the output piston in a hydraulic lift is increased while keeping the input force and input piston area constant, what happens to the output force?

Accepted Answer

The output force increases.

Question 9

A force of $$50\,\mathrm{N} is $$applied to a piston with area $$0.02\,\mathrm{m^2$}. $$What is the pressure exerted on the fluid?

Accepted Answer

$$1,000\,\mathrm{Pa}$$

Question 10

Which of the following statements about Pascal's Principle is correct?

Accepted Answer

A change in pressure at any point in a confined incompressible fluid is transmitted undiminished throughout the fluid.

Question 11

A cylindrical tank with a base radius of $$0.3\,\mathrm{m} is $$filled with a liquid to a height of $$1.2\,\mathrm{m}. If $$the liquid has a density of $$850\,\mathrm{kg/m^3$}$$, what is the force on the base due to the liquid? (Use $$g = 9.8\,\mathrm{m/s^2$})$$

Accepted Answer

$$F = 2,827\,\mathrm{N}$$

Question 12

If the pressure at the surface of a fluid is increased by $$5000\,\mathrm{Pa}$$, what is the change in pressure at a point $$2\,\mathrm{m}$$ below the surface?

Accepted Answer

The pressure increases by $$5000\,\mathrm{Pa}.$$

Question 13

A hydraulic press has an input piston of area $$0.005\,\mathrm{m^2$}$$ and an output piston of area $$0.2\,\mathrm{m^2$}. If a $$force of $$100\,\mathrm{N} is $$applied to the input piston, what is the pressure in the fluid?

Accepted Answer

$$20,000\,\mathrm{Pa}$$

Question 14

Which of the following is a real-world application of Pascal's Principle?

Accepted Answer

Hydraulic brakes in cars

Question 15

A fluid exerts a pressure of $$2,000\,\mathrm{Pa} on a $$surface of area $$0.5\,\mathrm{m^2$}. $$What is the force exerted by the fluid?

Accepted Answer

$$1,000\,\mathrm{N}$$

Fluid Mechanics: Pressure, Pascal's Principle, and Hydraulic Lifts

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