Q: Which of the following is a correct statement of Bernoulli's equation for a streamline in an ideal fluid?

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

Question 1

A block of wood with a density of $$600\ \mathrm{kg/m^3$}$$ and a volume of $$0.02\ \mathrm{m^3$} is $$fully submerged in water ($$\rho_{\mathrm{water}} = 1000\ \mathrm{kg/m^3$}). $$What is the magnitude of the buoyant force acting on the block?

Accepted Answer

$$F_B = 196\ \mathrm{N}$$

Question 2

Which of the following best describes the physical meaning of the buoyant force according to Archimedes' Principle?

Accepted Answer

It is equal to the weight of the fluid displaced by the object.

Question 3

A 45.0 g bird bone is weighed in air and then in water. Its apparent mass in water is 3.60 g. What is the volume of the bone?

Accepted Answer

$$V = 41.4\ \mathrm{cm^3$}$$

Question 4

A man has a mass of $$80\ \mathrm{kg}$$ and a density of $$955\ \mathrm{kg/m^3$}. $$What is his volume?

Accepted Answer

$$V = 0.084\ \mathrm{m^3$}$$

Question 5

Which equation expresses the condition for the continuity of an incompressible fluid flowing through a pipe with varying cross-sectional area?

Accepted Answer

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

Question 6

Blood flows through an artery that narrows from an area $$A_1 to$$ $$A_2$$ ($$A_2$$ \u003c $$A_1). If $$the velocity in the wider section is $$v_1$$, what is the velocity $$v_2 in $$the narrower section?

Accepted Answer

$$v_2$$ = $$v_1$$ \frac{$$A_1$$}{$$A_2$$}$$

Question 7

According to Bernoulli's equation, what happens to the pressure of a fluid as its speed increases in a horizontal pipe?

Accepted Answer

The pressure decreases.

Question 8

A fluid flows through a horizontal pipe. At point 1, the pressure is $$P_1$$ and the speed is $$v_1. At $$point 2, the pipe narrows and the speed increases to $$v_2. $$Using Bernoulli's equation, what is the pressure at point 2?

Accepted Answer

$$P_2$$ = $$P_1$$ - \frac{1}{2}\rho ($$v_2^2$$ - $$v_1^2$$)$$

Question 9

A submerged object appears to weigh less in water than in air. This is because:

Accepted Answer

The buoyant force acts upward, reducing the net force measured by the scale.

Question 10

A pipe carries water from a reservoir at height $$h_1 to a $$lower height $$h_2. If $$the water exits the pipe at atmospheric pressure and negligible velocity at the top, what is the exit speed $$v_2 at $$the bottom according to Bernoulli's theorem?

Accepted Answer

$$v_2$$ = \sqrt{2g($$h_1$$ - $$h_2$$)}$$

Question 11

Which of the following is a correct statement of Bernoulli's equation for a streamline in an ideal fluid?

Accepted Answer

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

Question 12

A left ventricle pumps blood at a flow rate of $$83.0\ \mathrm{cm^3$/s}$$, increasing its pressure by $$110\ \mathrm{mmHg}$$ and its speed from zero to $$30.0\ \mathrm{cm/s}. $$What is the total power output of the ventricle? (Assume $$1\ \mathrm{mmHg} = 133\ \mathrm{Pa}$$, $$\rho_{\mathrm{blood}} = 1060\ \mathrm{kg/m^3$})$$

Accepted Answer

$$1.22\ \mathrm{W}$$

Question 13

Which of the following best describes turbulent flow in a fluid?

Accepted Answer

Fluid particles move in chaotic, irregular paths with mixing.

Question 14

If the apparent mass of an object submerged in water is $$m'$$, and its true mass is $$m$$, what is the mass of water displaced?

Accepted Answer

$$m - m'$$

Question 15

A cube of side $$L is $$submerged in a fluid of density $$\rho. $$What is the difference in pressure between the top and bottom faces of the cube if the vertical height is $$L$$?

Accepted Answer

$$\Delta P = \rho g L$$

Question 16

Which of the following is NOT an assumption made in Bernoulli's equation?

Accepted Answer

The fluid is heated as it flows.

Question 17

A submarine is designed to have the same average density as seawater. What happens to the buoyant force if the submarine takes on water and increases its density?

Accepted Answer

The buoyant force remains the same, but the submarine sinks.

Question 18

A fluid flows steadily through a pipe that narrows from area $$A_1 to$$ $$A_2. If $$the density remains constant, which of the following is true about the volume flow rate?

Accepted Answer

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

Question 19

Which of the following real-life scenarios best illustrates Bernoulli's principle?

Accepted Answer

An airplane wing generating lift due to faster airflow above the wing.

Buoyancy and Hydrodynamics: Fluid Statics and Dynamics

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