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### Chapter 3.2 Notes

Rate in Fluids

Rates in fluid systems describe the motion of liquids and gases.

- Fluids in motion have speed and acceleration; however we use two different rates to describe how quickly fluids flow – volume flow rate and mass flow rate.

V represents the volume of fluid in a container.

- The volume flow rate is the change in volume per unit time.
- represents volume flow rate
- Equation for volume flow rate = change in volume / time

If the volume flow rate of the oxygen in the shuttle is 16,800 gallons per minute and the tank can hold 143,000 gallons, how long can the shuttle supply oxygen?

- Vfr = rV / t
- 16,800 gal/min = 143,000 gal / t
- t = 143,000 gal/min /16,800 gal
- t = 8.51 min

STOP!

Algebra Lesson

The mass flow rate is the mass of fluid moved per unit time.

- represents the mass flow rate
- The equation for mass flow rate = change in mass/time

If the shuttle’s fuel tank can hold 7000 grams of hydrogen and is consumed during the first 7 minutes of flight, what is the mass flow rate?

- Mfr = mass / time
- Mfr = 7000 grams / 7 min
- Mfr = 1000 grams/min

Methods for measuring volume and mass flow rates vary, depending on the situation.

- The simplest, most direct method to find average flow rate is to collect fluid and measure the amount of fluid collected over time.

Flowmeters measure the average flow rate of fluids by measuring pressure and velocity and calculating the flow rate.

- Flowmeters use indirect methods to measure flow rates so that they do not interrupt the flow.

Volume flow rate equation using speed = area x speed

- Mass flow rate equation using speed = density x area x speed
- To find cross sectional area of a pipe use this equation = pi x r2

If the pipe is 18 meters in diameter and the speed of the liquid is 24 m/s, what is the volume flow rate?

- A = pi x r2
- r = d/2 = 18/2 = 9 m
- A = 3.14 x 92 = 254.34 m2
- Vfr = Area x speed
- Vfr = 254.34 m2 x 24 m/s
- Vfr = 6104.16 m3/s

If the mass density is .5 g/L, the diameter of the pipe is 10 meters, and the speed is 190 m/s, what is the mass flow rate?

- A = pi x r2
- r = d/2 = 10/2 = 5 m
- A = 3.14 x 52 = 78.5 m2
- Vfr = Area x speed x density
- Vfr = 78.5 m2 x 190 m/s x .5 g/L
- Vfr = 7457.50 g/s

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