Q: A cylindrical rod of lead (density $$\rho_{\text{Pb}} = 11,300\ \mathrm{kg/m^3$}) $$with a diameter of $$14.0\ \mathrm{cm}$$ and height $$14.0\ \mathrm{cm} is $$suspended by a string and fully submerged in mercury (density $$\rho_{\text{Hg}} = 13,600\ \mathrm{kg/m^3$}). $$What is the tension in the string?

$$T = (\rho_{\text{Pb}} - \rho_{\text{Hg}}) V g$$

Q: A pipe with a $$6.0\ \mathrm{cm}$$ diameter carries water at a speed of $$2.0\ \mathrm{m/s}. $$What is the volume flow rate $$Q$$ through the pipe?

$$Q = A v = \pi (0.03)^2$ \times 2.0$$

Q: Water flows through a horizontal pipe that narrows from a diameter of $$8.0\ \mathrm{cm} to$$ $$4.0\ \mathrm{cm}. If $$the speed in the wider section is $$1.0\ \mathrm{m/s}$$, what is the speed in the narrower section?

$$v_2$$ = $$v_1$$ \frac{$$A_1$$}{$$A_2$$} = 1.0 \times \frac{$$(0.08/2)^2$$}{$$(0.04/2)^2$$}$$

Q: A cube of wood floats in water with $$60\% of $$its volume submerged. What is the density of the wood?

$$\rho_{\text{wood}} = 0.60 \rho_{\text{water}}$$

Q: A column of mercury is $$76.0\ \mathrm{cm}$$ high in a barometer at sea level. What is the atmospheric pressure in Pascals? (Density of mercury $$= 13,600\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

$$P = \rho g h = 13,600 \times 9.8 \times 0.76$$

Q: A block of unknown material floats in oil with $$80\% of $$its volume submerged. If the density of oil is $$900\ \mathrm{kg/m^3$}$$, what is the density of the block?

$$\rho_{\text{block}} = 0.80 \times 900$$

Q: A $$2.0\ \mathrm{cm}$$ diameter pipe carries water at $$3.0\ \mathrm{m/s}. $$What is the mass flow rate $$\dot{m} of $$water? (Density of water $$= 1000\ \mathrm{kg/m^3$})$$

$$\dot{m} = \rho A v = 1000 \times \pi (0.01)^2$ \times 3.0$$

Q: A column of air is $$1.0\ \mathrm{m}$$ tall and has a density of $$1.2\ \mathrm{kg/m^3$}. $$What is the pressure at the bottom of the column due to the air alone?

$$P = \rho g h = 1.2 \times 9.8 \times 1.0$$

Question 1

A cylindrical rod of lead (density $$ho_{	ext{Pb}} = 11,300\ \mathrm{kg/m^3$}) $$with a diameter of $$14.0\ \mathrm{cm}$$ and height $$14.0\ \mathrm{cm} is $$suspended by a string and fully submerged in mercury (density $$ho_{	ext{Hg}} = 13,600\ \mathrm{kg/m^3$}). $$What is the tension in the string?

Accepted Answer

$$T = (ho_{	ext{Pb}} - ho_{	ext{Hg}}) V g$$

Question 2

A pipe with a $$6.0\ \mathrm{cm}$$ diameter carries water at a speed of $$2.0\ \mathrm{m/s}. $$What is the volume flow rate $$Q$$ through the pipe?

Accepted Answer

$$Q = A v = \pi (0.03)^2$ 	imes 2.0$$

Question 3

Water flows through a horizontal pipe that narrows from a diameter of $$8.0\ \mathrm{cm} to$$ $$4.0\ \mathrm{cm}. If $$the speed in the wider section is $$1.0\ \mathrm{m/s}$$, what is the speed in the narrower section?

Accepted Answer

$$v_2$$ = $$v_1$$ \frac{$$A_1$$}{$$A_2$$} = 1.0 	imes \frac{$$(0.08/2)^2$$}{$$(0.04/2)^2$$}$$

Question 4

A fluid flows through a pipe with a varying diameter. If the pressure at the wider section is $$P_1$$ and at the narrower section is $$P_2$$, and the heights are the same, which equation correctly relates the pressures and speeds?

Accepted Answer

$$P_1$$ + \frac{1}{2} \rho $$v_1^2$$ = $$P_2$$ + \frac{1}{2} \rho $$v_2^2$

Question 5

A cube of wood floats in water with $$60\% of $$its volume submerged. What is the density of the wood?

Accepted Answer

$$ho_{	ext{wood}} = 0.60 ho_{	ext{water}}$$

Question 6

A column of mercury is $$76.0\ \mathrm{cm}$$ high in a barometer at sea level. What is the atmospheric pressure in Pascals? (Density of mercury $$= 13,600\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$P = ho g h = 13,600 	imes 9.8 	imes 0.76$$

Question 7

A block of unknown material floats in oil with $$80\% of $$its volume submerged. If the density of oil is $$900\ \mathrm{kg/m^3$}$$, what is the density of the block?

Accepted Answer

$$ho_{	ext{block}} = 0.80 	imes 900$$

Question 8

A lead puck (density $$11,300\ \mathrm{kg/m^3$}) is $$suspended in indium (density $$7,310\ \mathrm{kg/m^3$}) by a $$string. What is the buoyant force acting on the puck?

Accepted Answer

$$F_b = ho_{	ext{In}} V g$$

Question 9

A fluid flows steadily through a horizontal pipe. If the speed of the fluid increases, what happens to the pressure according to Bernoulli's principle?

Accepted Answer

The pressure decreases as the speed increases.

Question 10

A $$2.0\ \mathrm{cm}$$ diameter pipe carries water at $$3.0\ \mathrm{m/s}. $$What is the mass flow rate $$\dot{m} of $$water? (Density of water $$= 1000\ \mathrm{kg/m^3$})$$

Accepted Answer

$$\dot{m} = ho A v = 1000 	imes \pi (0.01)^2$ 	imes 3.0$$

Question 11

A very large tank is filled with water to a height $$h$$ above a small hole at the bottom. What is the speed of the water as it exits the hole?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 12

A column of air is $$1.0\ \mathrm{m}$$ tall and has a density of $$1.2\ \mathrm{kg/m^3$}. $$What is the pressure at the bottom of the column due to the air alone?

Accepted Answer

$$P = ho g h = 1.2 	imes 9.8 	imes 1.0$$

Question 13

A block is completely submerged in a fluid and is in equilibrium. Which of the following statements is true?

Accepted Answer

The buoyant force equals the weight of the block.

Question 14

A $$5.0\ \mathrm{cm}$$ diameter pipe narrows to $$2.5\ \mathrm{cm}. If $$the speed in the wider section is $$1.2\ \mathrm{m/s}$$, what is the speed in the narrower section?

Accepted Answer

$$v_2$$ = $$v_1$$ \frac{$$A_1$$}{$$A_2$$} = 1.2 	imes \frac{$$(0.05/2)^2$$}{$$(0.025/2)^2$$}$$

Question 15

A lead puck is suspended in indium. If the densities are $$ho_{	ext{Pb}} = 11,300\ \mathrm{kg/m^3$}$$ and $$ho_{	ext{In}} = 7,310\ \mathrm{kg/m^3$}$$, what is the apparent weight of the puck?

Accepted Answer

$$W_{	ext{apparent}} = (ho_{	ext{Pb}} - ho_{	ext{In}}) V g$$

Question 16

A fluid flows through a pipe that rises to a higher elevation. If the speed and pressure at the lower point are $$v_1$$ and $$P_1$$, and at the higher point are $$v_2$$ and $$P_2$$, what is the correct Bernoulli equation?

Accepted Answer

$$P_1$$ + \frac{1}{2} \rho $$v_1^2$$ + \rho g $$y_1$$ = $$P_2$$ + \frac{1}{2} \rho $$v_2^2$$ + \rho g $$y_2$$

Fluids: Homework Problems and Conceptual Applications

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