AP Physics 1: Algebra-Based Practice Quiz: Fluids and Conservation Laws

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 14 questions to check your progress.

Question 1 of 14

The continuity equation, A₁v₁ = A₂v₂, is a mathematical statement that describes which fundamental principle for an incompressible fluid?

A)Conservation of energyB)Conservation of massC)Conservation of momentumD)Conservation of charge

All Questions (14)

The continuity equation, A₁v₁ = A₂v₂, is a mathematical statement that describes which fundamental principle for an incompressible fluid?

A) Conservation of energy

B) Conservation of mass

C) Conservation of momentum

D) Conservation of charge

Correct Answer: B

The continuity equation states that the mass flow rate (mass per unit time) is constant throughout a pipe. For an incompressible fluid, where density is constant, this simplifies to the volume flow rate (Area × velocity) being constant, which is a direct result of the conservation of mass.

An incompressible fluid flows through a horizontal pipe that narrows to half of its original diameter. How does the speed of the fluid in the narrow section compare to its speed in the wide section?

A) It is half the speed.

B) It is twice the speed.

C) It is four times the speed.

D) It remains the same.

Correct Answer: C

The cross-sectional area A is proportional to the square of the diameter (or radius). If the diameter is halved, the area becomes (1/2)² = 1/4 of the original area. According to the continuity equation, A₁v₁ = A₂v₂, if the area A₂ is 1/4 of A₁, then the velocity v₂ must be 4 times v₁ to maintain the equality.

For a fluid flowing through a horizontal pipe of varying cross-sectional area, Bernoulli's equation predicts a relationship between fluid speed and pressure. What is this relationship?

A) Where the speed is higher, the pressure is higher.

B) Where the speed is higher, the pressure is lower.

C) Pressure is independent of the fluid's speed.

D) The ratio of pressure to speed is constant.

Correct Answer: B

In Bernoulli's equation, P + ρgy + ½ρv² = constant. For a horizontal pipe, the height y is constant, so the equation simplifies to P + ½ρv² = constant. This means that if the speed (v) increases, the pressure (P) must decrease to keep their sum constant.

A large, open-topped tank is filled with water. A small hole is punched in its side a distance 'h' below the water surface. According to Torricelli's theorem, what is the speed of the water as it exits the hole?

A) v = 2gh

B) v = gh

C) v = √(2gh)

D) v = √(gh/2)

Correct Answer: C

Torricelli's theorem, which is a special case of Bernoulli's equation, directly relates the exit speed of a fluid from an opening to the height of the fluid above the opening. The formula is v = √(2gh), where g is the acceleration due to gravity and h is the vertical distance from the fluid surface to the hole.

Water flows from a wide section of a horizontal pipe into a narrow section. Which statement correctly describes the changes in the fluid's speed and pressure?

A) Speed increases, pressure increases.

B) Speed decreases, pressure increases.

C) Speed increases, pressure decreases.

D) Speed decreases, pressure decreases.

Correct Answer: C

This requires combining two principles. First, the continuity equation (A₁v₁ = A₂v₂) dictates that as the area (A) decreases in the narrow section, the speed (v) must increase. Second, Bernoulli's equation for a horizontal pipe (P + ½ρv² = constant) dictates that where the speed (v) is higher, the pressure (P) must be lower.

The flow of a fluid from a region of higher potential energy to a region of lower potential energy within the fluid-Earth system is a direct consequence of which principle?

A) Conservation of mass

B) Conservation of energy

C) Newton's Third Law

D) The Ideal Gas Law

Correct Answer: B

The provided content states that fluid flow is a result of a difference in energy between two locations. Systems naturally tend to move from higher energy states to lower energy states. This energy difference can be due to pressure, height (gravitational potential energy), or speed (kinetic energy).

Torricelli's theorem is a simplified application of Bernoulli's equation. What key assumption is made when deriving v = √(2gh) from the full Bernoulli's equation for a large tank with a small hole?

A) The fluid is compressible.

B) The pressure outside the hole is zero.

C) The velocity of the fluid at the top surface is negligible (approximately zero).

D) The acceleration due to gravity is not constant.

Correct Answer: C

To derive Torricelli's theorem, we apply Bernoulli's equation between the top surface (point 1) and the hole (point 2). We assume P₁ = P₂ (both are at atmospheric pressure) and that for a large tank, the surface level drops very slowly, so v₁ ≈ 0. The equation P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂² simplifies to ρgy₁ = ρgy₂ + ½ρv₂², which rearranges to v₂ = √(2g(y₁-y₂)) or v = √(2gh).

For an incompressible fluid in steady flow through a pipe, the mass of fluid passing a point in the wide section of the pipe in one second is ________ the mass of fluid passing a point in the narrow section in one second.

A) greater than

B) less than

C) equal to

D) proportional to the area of

Correct Answer: C

This is a direct statement of the principle of mass conservation. In steady flow, mass is not created or destroyed within the pipe, so the mass flow rate (mass per unit time) must be constant at all points along the pipe, regardless of its cross-sectional area.

In Bernoulli's equation, P + ρgy + ½ρv² = constant, what physical quantity does the term ½ρv² represent?

A) The work done by gravity per unit volume.

B) The pressure exerted by the fluid.

C) The gravitational potential energy per unit volume.

D) The kinetic energy per unit volume.

Correct Answer: D

The term for kinetic energy is ½mv². Since density ρ = m/V (mass/volume), we can write m = ρV. Substituting this into the kinetic energy formula gives ½(ρV)v². The kinetic energy per unit volume is then (½ρVv²)/V = ½ρv².

A horizontal pipe has a cross-sectional area of A₁ and the fluid has a speed v₁. The pipe narrows to an area A₂ = A₁/4. If the pressure at the first point is P₁, what is the pressure P₂ in the narrow section?

A) P₁ - (15/2)ρv₁²

B) P₁ + (15/2)ρv₁²

C) P₁ - (3/2)ρv₁²

D) P₁ - 8ρv₁²

Correct Answer: A

First, use the continuity equation: A₁v₁ = A₂v₂ → A₁v₁ = (A₁/4)v₂ → v₂ = 4v₁. Next, use Bernoulli's equation for a horizontal pipe: P₁ + ½ρv₁² = P₂ + ½ρv₂². Substitute v₂ = 4v₁: P₁ + ½ρv₁² = P₂ + ½ρ(4v₁)² = P₂ + ½ρ(16v₁²) = P₂ + 8ρv₁². Solve for P₂: P₂ = P₁ + ½ρv₁² - 8ρv₁² = P₁ - (15/2)ρv₁².

Two large, open water tanks are identical, but the water level in Tank A is 9 times higher than in Tank B. A small hole is opened at the bottom of each tank. How does the exit speed of the water from Tank A (v_A) compare to that from Tank B (v_B)?

A) v_A = 9 * v_B

B) v_A = 81 * v_B

C) v_A = 3 * v_B

D) v_A = v_B

Correct Answer: C

According to Torricelli's theorem, exit speed v = √(2gh). This means that the speed is proportional to the square root of the height (v ∝ √h). If h_A = 9 * h_B, then v_A will be proportional to √9 = 3 times v_B.

Water is flowing upwards through a vertical pipe with a constant diameter. Comparing a point lower in the pipe (point 1) to a point higher up (point 2), what can be concluded about the pressure?

A) The pressure is the same at both points because the velocity is constant.

B) The pressure is greater at the higher point (P₂ > P₁).

C) The pressure is greater at the lower point (P₁ > P₂).

D) The relationship cannot be determined without the fluid density.

Correct Answer: C

Since the diameter is constant, the continuity equation implies the velocity is constant (v₁ = v₂). Bernoulli's equation is P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂². The kinetic energy terms cancel out. This leaves P₁ + ρgy₁ = P₂ + ρgy₂. Since y₂ > y₁, the term ρgy₂ is larger than ρgy₁. To maintain the equality, P₁ must be greater than P₂.

Which equation is the mathematical representation of the conservation of mechanical energy for an ideal fluid in motion?

A) A₁v₁ = A₂v₂

B) v = √(2gh)

C) P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂²

D) ρ = m/V

Correct Answer: C

The content explicitly states that Bernoulli’s equation (P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂²) describes the conservation of mechanical energy in fluid flow. The terms represent pressure energy, potential energy, and kinetic energy per unit volume.

A large, open water tank has its surface at a height of 50 m above the ground. A pipe with a constant diameter extends from the bottom of the tank to an outlet 10 m above the ground. What is the speed of the water as it exits the pipe? (Assume the pressure at the tank surface and the outlet are both atmospheric pressure).

A) √(2g * 10m)

B) √(2g * 40m)

C) √(2g * 50m)

D) √(2g * 60m)

Correct Answer: B

This is an application of Bernoulli's equation, which simplifies to Torricelli's theorem for this case. Let point 1 be the water surface and point 2 be the outlet. P₁ = P₂ (atmospheric), and v₁ ≈ 0. The equation becomes ρgy₁ = ρgy₂ + ½ρv₂². Solving for v₂ gives v₂ = √(2g(y₁-y₂)). The height difference (y₁-y₂) is 50 m - 10 m = 40 m. Therefore, the exit speed is √(2g * 40m).