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Chapter 3.2 Notes

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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

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