Q: Bernoulli's equation for a streamline flow is given by:

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

Question 1

A block of wood floats in water. If the density of the wood is $$600 \ \mathrm{kg/m^3$}$$ and the density of water is $$1000 \ \mathrm{kg/m^3$}$$, what fraction of the block's volume is submerged?

Accepted Answer

$$0.60$$

Question 2

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

Accepted Answer

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

Question 3

Which of the following best describes the buoyant force acting on an object submerged in a fluid?

Accepted Answer

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

Question 4

A bird bone has a mass of $$45.0 \ \mathrm{g} in $$air and an apparent mass of $$36.0 \ \mathrm{g}$$ when submerged in water. What is the volume of the bone?

Accepted Answer

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

Question 5

Which equation represents the condition for incompressible fluid flow according to the equation of continuity?

Accepted Answer

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

Question 6

A pipe narrows from an area $$A_1 to$$ $$A_2$$ and the fluid speeds up from $$v_1 to$$ $$v_2. If $$the fluid is incompressible, which of the following is true?

Accepted Answer

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

Question 7

Bernoulli's equation for a streamline flow is given by:

Accepted Answer

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

Question 8

A fluid flows through a horizontal pipe that narrows. What happens to the fluid's speed and pressure in the narrow section?

Accepted Answer

Speed increases, pressure decreases.

Question 9

The left ventricle of a heart pumps blood at a flow rate of $$83.0 \ \mathrm{cm^3$/s}$$, increasing its pressure by $$110 \ \mathrm{mmHg}. $$What is the power output if most of the power is used to increase blood pressure? (Use $$1 \ \mathrm{mmHg} = 1.33 	imes 10^2$ \ \mathrm{Pa})$$

Accepted Answer

$$1.27 \ \mathrm{W}$$

Question 10

Which of the following is a correct statement of Archimedes' Principle?

Accepted Answer

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

Question 11

A submerged object experiences a buoyant force $$F_B$$ given by:

Accepted Answer

$$F_B = \rho_{fluid} g V_{displaced}$$

Question 12

A bone is weighed in air and then submerged in water. Its mass in air is $$45.0 \ \mathrm{g}$$ and its apparent mass in water is $$36.0 \ \mathrm{g}. $$What is the mass of water displaced?

Accepted Answer

$$9.0 \ \mathrm{g}$$

Question 13

Which of the following best describes laminar flow?

Accepted Answer

Fluid particles move in smooth, parallel layers.

Question 14

According to Bernoulli's theorem, what happens to the pressure in a region where the fluid speed increases?

Accepted Answer

Pressure decreases.

Question 15

A horizontal pipe carries water at a speed $$v_1 in a $$wide section and $$v_2 in a $$narrow section. If the pressure in the wide section is $$P_1$$, what is the pressure $$P_2 in $$the narrow section according to Bernoulli's equation?

Accepted Answer

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

Question 16

Which of the following is a consequence of the equation of continuity for an incompressible fluid?

Accepted Answer

The product of cross-sectional area and velocity is constant along the pipe.

Question 17

A fluid flows through a pipe with cross-sectional area $$A_1$$ and velocity $$v_1 at $$one end, and $$A_2$$ and $$v_2 at $$the other. If the fluid is incompressible, which equation must be satisfied?

Accepted Answer

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

Question 18

In the context of Bernoulli's equation, which term represents the kinetic energy per unit volume of the fluid?

Accepted Answer

$$\frac{1}{2} \rho v^2$

Buoyancy and Hydrodynamics: Buoyant Forces, Fluid Flow, and Bernoulli’s Theorem

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