AP Physics 1 Bernoulli and continuity equations practice questions

What does Bernoulli's equation relate to?

The relationship between pressure, velocity, and height in a fluid flow.

True or False: Pressure increases as fluid velocity decreases in Bernoulli's principle.

True. This is a consequence of energy conservation in fluid dynamics.

Fill in the blank: In Bernoulli's equation, the total energy is the sum of ______, kinetic, and potential energy.

pressure energy.

What is the formula for Bernoulli's equation?

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

Cause → Effect: Increase in fluid speed leads to ______ pressure according to Bernoulli's principle.

decreased pressure.

How does Bernoulli's principle explain airplane lift?

Air travels faster over the wing, creating lower pressure on top, causing lift.

What is the effect of pipe narrowing on fluid velocity?

Velocity increases as the cross-sectional area decreases, according to the continuity equation.

True or False: Bernoulli's equation can be applied to both incompressible and compressible fluids.

False. It primarily applies to incompressible fluids.

Compare: Bernoulli’s principle vs. Continuity equation.

Bernoulli's principle focuses on energy conservation; continuity equation focuses on mass flow rates.

Question: What happens to pressure in a constricted flow area?

Pressure decreases as velocity increases in the constricted region.

What do we call a situation where Bernoulli's principle applies?

Streamlined flow in an ideal fluid.

Fill in the blank: The term for the energy per unit volume in Bernoulli's equation is ______.

pressure energy.

What are the units of pressure in Bernoulli's equation?

Pascals (Pa) or pounds per square inch (psi).

How does Bernoulli's principle relate to a garden hose nozzle?

As water flows through the nozzle, it speeds up, causing pressure to drop, increasing velocity.

True or False: Bernoulli's principle implies that fluid moves from low to high pressure areas.

False. Fluid moves from high to low pressure areas.

What does Bernoulli's principle imply about fluid potential energy?

Fluid potential energy decreases as kinetic energy increases in horizontal flow.

Define the continuity equation.

The continuity equation states that for an incompressible fluid, the mass flow rate must remain constant from one cross-section to another: $\displaystyle A_1v_1 = A_2v_2$.

True or False: Fluid velocity increases as the cross-sectional area decreases.

True. According to the continuity equation, as area decreases, velocity must increase to maintain a constant flow rate.

Calculate the flow velocity if A1 = 2 m², A2 = 1 m², and v1 = 3 m/s.

Using $\displaystyle A_1v_1 = A_2v_2$: $\displaystyle 2 ext{ m}^2(3 ext{ m/s}) = 1 ext{ m}^2(v_2)$ $\displaystyle 6 = v_2$ $\displaystyle v_2 = 6 ext{ m/s}$.

Fill in the blank: The continuity equation applies to _________ fluids.

incompressible.

List factors that affect flow rate in the continuity equation.

- Cross-sectional area - Fluid velocity - Density (for compressible fluids) For incompressible fluids, density is constant.

Describe the relationship between A1, A2, v1, and v2 in the continuity equation.

If $\displaystyle A_1 > A_2$, then $\displaystyle v_1 < v_2$. This shows that if the area decreases, fluid velocity increases.

How does the continuity equation relate to pipe flow?

In pipe flow, varying diameters create changes in velocity. For constant flow rate, smaller diameters increase velocity.

True or False: The continuity equation can be applied to compressible fluids without modifications.

False. For compressible fluids, the density must be considered alongside the area and velocity.

Given A1 = 3 ft², A2 = 1 ft², and v1 = 5 ft/s, find v2.

Using the continuity equation: $\displaystyle 3 ext{ ft}^2(5 ext{ ft/s}) = 1 ext{ ft}^2(v_2)$ $\displaystyle v_2 = 15 ext{ ft/s}$.

What happens to flow rate if A1 = A2?

If $\displaystyle A_1 = A_2$, then $\displaystyle v_1 = v_2$. The flow rate remains constant.

Explain the principle of conservation in the continuity equation.

The continuity equation is based on the conservation of mass. The mass that enters a region must equal the mass that exits.

Identify what the variables A and v represent in the equation: $\displaystyle A_1v_1 = A_2v_2$.

A represents the cross-sectional area, and v represents the fluid velocity.

What is the impact of a narrowing pipe on fluid pressure?

According to Bernoulli’s principle, as the pipe narrows and velocity increases, pressure decreases.

List two applications of the continuity equation.

- Blood flow in arteries - Airflow in ducts - Water flow in hoses

True or False: The continuity equation applies regardless of fluid viscosity.

True. The continuity equation is concerned with flow rate and cross-sectional area, not viscosity.

Explain why the continuity equation is essential in engineering.

Engineers use the continuity equation to design systems like pipes and channels, ensuring consistent flow rates and avoiding blockages.

Describe the relationship between velocity and cross-sectional area.

According to the continuity equation, as cross-sectional area decreases, velocity increases: - $\displaystyle \frac{A_1 v_1}{A_2 v_2}$ - $\displaystyle A_1 v_1 = A_2 v_2$.

True or false: Bernoulli's principle applies to non-incompressible fluids.

True. Bernoulli's principle is valid for incompressible fluids, where density remains constant.

Fill in the blank: In a horizontal pipe, as __________ decreases, pressure increases.

velocity.

Explain how Bernoulli’s principle applies in an airplane wing.

Air moves faster over the wing, reducing pressure above and creating lift. - Velocity increase - Pressure difference - Lift generation.

If area decreases, what happens to pressure according to Bernoulli's principle?

Pressure decreases. This is due to the conservation of energy in fluid flow.

Calculate the velocity of water at a narrower section of a pipe.

Given: - $\displaystyle A_1 = 4 ext{ ft}^2$, $\displaystyle A_2 = 2 ext{ ft}^2$, $\displaystyle v_1 = 3 ext{ ft/s}$. - Use $\displaystyle A_1 v_1 = A_2 v_2$. - $\displaystyle v_2 = \frac{A_1 v_1}{A_2} = \frac{4 imes 3}{2} = 6 ext{ ft/s}$.

Compare dynamic and static pressure in Bernoulli's equation.

Dynamic pressure (kinetic energy per unit volume) and static pressure (potential energy per unit volume) relate inversely. - Increase in dynamic pressure - Decrease in static pressure.

What happens to fluid velocity when the cross-sectional area of a pipe halves?

Velocity doubles, according to the continuity equation.

True or false: In Bernoulli's equation, total energy remains constant.

True. Total mechanical energy of the fluid remains constant in steady, incompressible flow.

Predict the effect on pressure when fluid flows through a tapered pipe.

Pressure decreases as fluid velocity increases in the narrower section due to Bernoulli’s principle.

Calculate the change in pressure in a horizontal pipe with varying diameter.

Given: - $\displaystyle v_1 = 5 ext{ m/s}$, $\displaystyle v_2 = 10 ext{ m/s}$, with fluid density $\displaystyle ho = 1000 ext{ kg/m}^3$. - Use Bernoulli's equation: $\displaystyle \frac{1}{2} ho v_1^2 + P_1 = \frac{1}{2} ho v_2^2 + P_2$. - Solve for $\displaystyle P_1 - P_2$.

True or false: Continuity equation applies to compressible fluids.

False. The continuity equation is primarily used for incompressible fluid flow.

How does Bernoulli's principle explain a garden hose nozzle?

In a nozzle, area decreases, causing velocity to increase and pressure to decrease, resulting in a faster water stream.

What is the relationship between flow rate and pipe diameter?

Flow rate is directly proportional to the square of the diameter, assuming constant velocity.

Fill in the blank: Bernoulli's equation relates __________ to kinetic and potential energy.

pressure.

Explain the application of both principles in a Venturi meter.

A Venturi meter measures fluid flow rate: - Pressure difference indicates flow rate. - Area decreases, velocity increases, and pressure decreases.