Fluids — Practice Quiz

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

Formulas & key concepts

Mass Density: Mass \(m\) per unit volume \(V\).

$$\rho = \frac{m}{V}$$

Where: \(\rho\) = density

Pressure: Force \(F\) applied perpendicular to area \(A\).

$$P = \frac{F}{A}$$

Pressure with Depth: Pressure \(P_2\) at depth \(h\) below a point with pressure \(P_1\) in a fluid of density \(\rho\).

$$P_2 = P_1 + \rho gh$$

Pascal's Principle: Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid.

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

Archimedes' Principle: Buoyant force \(F_B\) equals the weight of the displaced fluid.

$$F_B = \rho g V$$

Equation of Continuity: For incompressible fluid flow, the flow rate is constant.

$$A_1 v_1 = A_2 v_2$$

Bernoulli's Equation: Relates pressure, speed, and height for fluid flow.

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

Practice quiz

  1. A block of wood has a mass of $1200 \text{ kg}$ and a volume of $1.5 \text{ m}^3$. What is its density?

    • A) $800 \text{ kg/m}^3$
    • B) $1800 \text{ kg/m}^3$
    • C) $0.00125 \text{ kg/m}^3$
    • D) $1200 \text{ kg/m}^3$

    Answer: A) $800 \text{ kg/m}^3$

  2. A force of $500 \text{ N}$ is applied perpendicularly to a surface with an area of $0.25 \text{ m}^2$. What is the pressure exerted on the surface?

    • A) $125 \text{ Pa}$
    • B) $2000 \text{ Pa}$
    • C) $500 \text{ Pa}$
    • D) $0.0005 \text{ Pa}$

    Answer: B) $2000 \text{ Pa}$

  3. What is the gauge pressure at a depth of $10 \text{ m}$ in water? (Assume density of water is $1000 \text{ kg/m}^3$ and $g = 9.8 \text{ m/s}^2$).

    • A) $9800 \text{ Pa}$
    • B) $98000 \text{ Pa}$
    • C) $100000 \text{ Pa}$
    • D) $10000 \text{ Pa}$

    Answer: B) $98000 \text{ Pa}$

  4. In a hydraulic lift, a force of $100 \text{ N}$ is applied to a small piston with an area of $0.01 \text{ m}^2$. If the large piston has an area of $0.5 \text{ m}^2$, what is the maximum load it can lift?

    • A) $500 \text{ N}$
    • B) $5000 \text{ N}$
    • C) $1000 \text{ N}$
    • D) $2000 \text{ N}$

    Answer: B) $5000 \text{ N}$

  5. An object with a volume of $0.02 \text{ m}^3$ is fully submerged in a fluid with a density of $800 \text{ kg/m}^3$. What is the buoyant force acting on the object? (Assume $g = 9.8 \text{ m/s}^2$).

    • A) $156.8 \text{ N}$
    • B) $160 \text{ N}$
    • C) $196 \text{ N}$
    • D) $1568 \text{ N}$

    Answer: A) $156.8 \text{ N}$

  6. Water flows through a pipe with a cross-sectional area of $0.1 \text{ m}^2$ at a speed of $2 \text{ m/s}$. If the pipe narrows to an area of $0.02 \text{ m}^2$, what is the speed of the water in the narrower section?

    • A) $0.4 \text{ m/s}$
    • B) $10 \text{ m/s}$
    • C) $2 \text{ m/s}$
    • D) $5 \text{ m/s}$

    Answer: B) $10 \text{ m/s}$

  7. According to Bernoulli's principle, if the speed of an incompressible fluid increases in a horizontal pipe, what happens to its pressure?

    • A) It increases.
    • B) It decreases.
    • C) It remains constant.
    • D) It depends on the fluid's density.

    Answer: B) It decreases.

  8. A submarine dives to a depth where the pressure is $2.026 \times 10^5 \text{ Pa}$ greater than the surface pressure. If the density of seawater is $1025 \text{ kg/m}^3$ and $g = 9.8 \text{ m/s}^2$, what is the depth of the submarine?

    • A) $10 \text{ m}$
    • B) $20 \text{ m}$
    • C) $15 \text{ m}$
    • D) $5 \text{ m}$

    Answer: B) $20 \text{ m}$

  9. A solid object weighs $50 \text{ N}$ in air and $30 \text{ N}$ when fully submerged in water (density $1000 \text{ kg/m}^3$). What is the volume of the object? (Assume $g = 9.8 \text{ m/s}^2$).

    • A) $0.00204 \text{ m}^3$
    • B) $0.00306 \text{ m}^3$
    • C) $0.00510 \text{ m}^3$
    • D) $0.00102 \text{ m}^3$

    Answer: A) $0.00204 \text{ m}^3$

  10. A large water tank has a small hole at its bottom. Water flows out of the hole. If the water level in the tank is $5 \text{ m}$ above the hole, what is the approximate speed of the water exiting the hole? (Assume atmospheric pressure at both the surface and the hole, and $g = 9.8 \text{ m/s}^2$).

    • A) $9.9 \text{ m/s}$
    • B) $7.0 \text{ m/s}$
    • C) $14.0 \text{ m/s}$
    • D) $4.9 \text{ m/s}$

    Answer: A) $9.9 \text{ m/s}$

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