Continuity Equation and Fluid Dynamics

Mr. Andersen explains the continuity equation, an application of the conservation of mass in fluids. He discusses how changes in the diameter of a fire hose affect velocity, using the continuity equation to demonstrate mass and volume flow rates. A PHET simulation illustrates how decreasing cross-sectional area increases velocity. A problem-solving example shows how to calculate velocity changes using geometry and the continuity equation.

What fundamental principle is the continuity equation based on?

• Conservation of charge

• Conservation of mass

• Conservation of momentum

• Conservation of energy

How does the continuity equation relate to the mass flow rate?

• It equates mass flow rate to momentum flow rate.

• It equates mass flow rate to energy flow rate.

• It equates mass flow rate to charge flow rate.

• It equates mass flow rate to volume flow rate.

Which of the following is NOT a component of the continuity equation?

• Velocity of the fluid

• Cross-sectional area

• Density of the fluid

• Temperature of the fluid

What happens to the velocity of a fluid if the cross-sectional area decreases?

• Velocity decreases

• Velocity becomes zero

• Velocity remains constant

• Velocity increases

In the continuity equation, what does A1 V1 = A2 V2 represent?

• Energy conservation

• Mass conservation

• Charge conservation

• Momentum conservation

If the cross-sectional area of a pipe is 10 m² and the velocity is 0.5 m/s, what is the product of area and velocity?

• 20

• 0.5

• 10

• 5

What is the velocity of water coming out of a nozzle if the diameter is reduced to 2.3 cm from 7.5 cm?

• 4 m/s

• 10 m/s

• 100 m/s

• 43 m/s

How do you calculate the cross-sectional area from the diameter?

• Using the formula πd²

• Using the formula πd

• Using the formula πr²

• Using the formula 2πr

What is the first step in solving for velocity using the continuity equation?

• Convert velocity to area

• Convert diameter to radius

• Convert area to diameter

• Convert radius to diameter

What is the approximate velocity of water in the hose before it exits the nozzle?

• 10 m/s

• 43 m/s

• 4 m/s

• 100 m/s