Fluids — Hard Practice Quiz

A Physics cheat sheet for Fluids — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Practice quiz

1. A solid object floats in water with $80\%$ of its volume submerged. If this object is placed in an unknown liquid, $90\%$ of its volume is submerged. What is the density of the unknown liquid, given that the density of water is $1000 \text{ kg/m}^3$?

   • $888.9 \text{ kg/m}^3$
   • $1125 \text{ kg/m}^3$
   • $720 \text{ kg/m}^3$
   • $900 \text{ kg/m}^3$

   Answer: $888.9 \text{ kg/m}^3$

2. Water flows through a horizontal pipe with a cross-sectional area of $A_1 = 0.05 \text{ m}^2$ at a speed of $v_1 = 2 \text{ m/s}$ and a pressure of $P_1 = 200 \text{ kPa}$. The pipe then narrows to an area of $A_2 = 0.02 \text{ m}^2$ and rises to a height of $h_2 = 5 \text{ m}$ above the initial level ($h_1 = 0$). Assuming the density of water is $1000 \text{ kg/m}^3$ and $g = 9.8 \text{ m/s}^2$, what is the pressure $P_2$ in the narrower, elevated section?

   • $140.5 \text{ kPa}$
   • $152.5 \text{ kPa}$
   • $187.5 \text{ kPa}$
   • $214.5 \text{ kPa}$

   Answer: $140.5 \text{ kPa}$

3. A hydraulic lift system has an input piston of area $A_1 = 0.01 \text{ m}^2$ and an output piston of area $A_2 = 0.5 \text{ m}^2$. The entire system is submerged in a large tank of oil with density $800 \text{ kg/m}^3$. The input piston is $2 \text{ m}$ deeper than the output piston. If a force of $F_1 = 100 \text{ N}$ is applied to the input piston, what is the maximum load $F_2$ that can be lifted by the output piston? Assume $g = 9.8 \text{ m/s}^2$.

   • $12840 \text{ N}$
   • $5000 \text{ N}$
   • $10000 \text{ N}$
   • $17840 \text{ N}$

   Answer: $12840 \text{ N}$

4. Consider an incompressible fluid flowing horizontally through a pipe that narrows. If the fluid's speed increases in the narrower section, what can be concluded about the pressure in that section, assuming no significant height change?

   • The pressure decreases.
   • The pressure increases.
   • The pressure remains constant.
   • The pressure change depends on the fluid's density.

   Answer: The pressure decreases.

5. A solid block of volume $V = 0.02 \text{ m}^3$ has a mass of $m = 15 \text{ kg}$. It is fully submerged in a liquid with density $\rho_{liquid} = 900 \text{ kg/m}^3$. What is the apparent weight of the block when submerged? Assume $g = 9.8 \text{ m/s}^2$. (A negative value indicates an upward force).

   • $147 \text{ N}$
   • $176.4 \text{ N}$
   • $-29.4 \text{ N}$
   • $323.4 \text{ N}$

   Answer: $-29.4 \text{ N}$

6. A siphon is used to drain water from a large open tank. The water level in the tank is $H = 5 \text{ m}$ above the ground. The highest point of the siphon tube is $h_1 = 2 \text{ m}$ above the water level in the tank. The outlet of the siphon is $h_2 = 1 \text{ m}$ above the ground. What is the speed of the water as it exits the siphon? Assume atmospheric pressure at the surface and outlet, density of water is $1000 \text{ kg/m}^3$, and $g = 9.8 \text{ m/s}^2$.

   • $8.85 \text{ m/s}$
   • $9.90 \text{ m/s}$
   • $10.84 \text{ m/s}$
   • $12.12 \text{ m/s}$

   Answer: $8.85 \text{ m/s}$

7. A solid block of mass $M$ and volume $V$ is placed on a small piston of area $A_1$ in a hydraulic system. The system is filled with a fluid of density $\rho_f$. The large piston has area $A_2$. If the block is then fully submerged in the fluid (but still resting on the small piston), how does the force $F_2$ on the large piston change compared to when the block was above the fluid?

   • It increases by $\frac{\rho_f g V A_2}{A_1}$.
   • It decreases by $\frac{\rho_f g V A_2}{A_1}$.
   • It remains the same.
   • It decreases by $\rho_f g V$.

   Answer: It decreases by $\frac{\rho_f g V A_2}{A_1}$.

8. Water flows through a horizontal pipe. At point A, the pipe has a radius $r_A$ and the water speed is $v_A$. At point B, the pipe narrows to a radius $r_B = r_A/2$. What is the ratio of the pressure difference $(P_A - P_B)$ to the dynamic pressure at point A ($\frac{1}{2}\rho v_A^2$)?

   • $15$
   • $3$
   • $7$
   • $16$

   Answer: $15$

9. A cylindrical tank contains two immiscible liquids. The bottom layer has a height of $h_1 = 1.5 \text{ m}$ and density $\rho_1 = 1200 \text{ kg/m}^3$. The top layer has a height of $h_2 = 2.0 \text{ m}$ and density $\rho_2 = 800 \text{ kg/m}^3$. What is the absolute pressure at the bottom of the tank if the atmospheric pressure at the surface is $P_{atm} = 101325 \text{ Pa}$? Assume $g = 9.8 \text{ m/s}^2$.

   • $134645 \text{ Pa}$
   • $116965 \text{ Pa}$
   • $118965 \text{ Pa}$
   • $101325 \text{ Pa}$

   Answer: $134645 \text{ Pa}$

10. A sealed tank contains a gas at a pressure of $P_{gas} = 200 \text{ kPa}$ above a liquid of density $\rho_L = 1200 \text{ kg/m}^3$. A solid sphere of volume $V = 0.01 \text{ m}^3$ and mass $m = 8 \text{ kg}$ is fully submerged in the liquid. What is the tension in a string holding the sphere to the bottom of the tank? Assume $g = 9.8 \text{ m/s}^2$.

    • $39.2 \text{ N}$
    • $78.4 \text{ N}$
    • $117.6 \text{ N}$
    • $196.0 \text{ N}$

    Answer: $39.2 \text{ N}$