Q: Bernoulli’s equation relates pressure, velocity, and height in a flowing fluid. Which of the following is the correct form of Bernoulli’s equation?

$$P + \frac{1}{2} \rho v^2$ + \rho g h = \text{constant}$$

Question 1

Which of the following best describes why atmospheric pressure does not crush us, even though it is about $$1.01 	imes 10^5$ N/m^2$ at sea level?

Accepted Answer

Our cells contain an internal pressure that balances the external atmospheric pressure.

Question 2

A sealed straw is filled with water and held vertically. If you place your finger over the top and lift the straw out of the water, what happens to the water inside the straw?

Accepted Answer

Most of the water remains in the straw due to the pressure difference between the inside and outside air.

Question 3

Which equation correctly expresses the pressure at a depth $$h in a $$fluid of density $$\rho$$ under gravity $$g$$?

Accepted Answer

$$P = P_0$ + \rho g h$$

Question 4

A bucket with a hole in its side is dropped in free fall. What happens to the water flowing out of the hole?

Accepted Answer

The water flow stops altogether because the pressure difference vanishes in free fall.

Question 5

According to Pascal’s Principle, what happens when an external pressure is applied to a confined fluid?

Accepted Answer

The pressure increases equally at every point within the fluid.

Question 6

A boat carrying a large chunk of steel is floating on a lake. The chunk is thrown overboard and sinks. What happens to the water level in the lake?

Accepted Answer

The water level drops.

Question 7

An object floats in water with $$\frac{2}{3} of $$its volume submerged. What is the ratio of the density of the object $$\rho_{obj} to $$the density of water $$\rho_{water}$$?

Accepted Answer

$$\frac{\rho_{obj}}{\rho_{water}} = \frac{2}{3}$$

Question 8

If an object floats in water and is then placed in oil with half the density of water, what happens?

Accepted Answer

It sinks to the bottom.

Question 9

Which of the following is the correct statement of Archimedes’ Principle?

Accepted Answer

The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.

Question 10

A fluid flows through a pipe that narrows from a diameter of 2 cm to 1 cm. If the speed in the wider section is $$v$$, what is the speed in the narrower section?

Accepted Answer

$$4v$$

Question 11

Which equation represents the continuity equation for an incompressible fluid flowing through a pipe?

Accepted Answer

$$A_1$$ $$v_1$$ = $$A_2$$ $$v_2$$

Question 12

Bernoulli’s equation relates pressure, velocity, and height in a flowing fluid. Which of the following is the correct form of Bernoulli’s equation?

Accepted Answer

$$P + \frac{1}{2} ho v^2$ + ho g h = 	ext{constant}$$

Question 13

According to Bernoulli’s principle, what happens to the pressure in a region where the fluid velocity is high?

Accepted Answer

The pressure is low.

Question 14

A ball curves in flight due to its spin. What physical principle explains this phenomenon?

Accepted Answer

Bernoulli’s principle, which states that a pressure difference is created by different air speeds on each side of the ball.

Question 15

Smoke rises more rapidly up a chimney when there is a wind blowing outside. What principle explains this?

Accepted Answer

Bernoulli’s principle: the wind lowers the pressure at the top of the chimney, increasing the upward flow.

Question 16

A hydraulic lift uses a small piston of area $$A_1$$ and a large piston of area $$A_2. If a $$force $$F_1 is $$applied to the small piston, what is the force $$F_2$$ exerted by the large piston?

Accepted Answer

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

Question 17

A helium balloon of volume $$V is $$used to lift a payload of mass $$m_{load}. If $$the density of air is $$\rho_{air}$$ and the density of helium is $$\rho_{He}$$, what is the minimum volume $$V$$ required to lift the payload?

Accepted Answer

$$V = \frac{m_{load}}{\rho_{air} - \rho_{He}}$$

Question 18

Which of the following best describes viscosity in fluids?

Accepted Answer

Viscosity is a measure of a fluid’s internal friction, which resists flow.

Question 19

A Venturi meter measures fluid flow by comparing pressure differences at two points. If the cross-sectional area at point 1 is $$A_1$$ and at point 2 is $$A_2$$, and the fluid speeds are $$v_1$$ and $$v_2$$, which equation relates the speeds and areas?

Accepted Answer

$$A_1$$ $$v_1$$ = $$A_2$$ $$v_2$$

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