Chapter 3.2 Chapter 3.2 NotesNotes

Rate in FluidsRate in Fluids

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

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

V represents the V represents the volumevolume of of fluid in a container.fluid in a container.

The The volume flow ratevolume flow rate is the is the change in volume per unit change in volume per unit time.time.

represents volume flow raterepresents volume flow rate Equation for volume flow rate = Equation for volume flow rate =

change in volume / timechange in volume / time

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

Vfr = Vfr = V / tV / t 16,800 gal/min = 143,000 gal / t16,800 gal/min = 143,000 gal / t t = 143,000 gal/min t = 143,000 gal/min //16,800 gal16,800 gal t = t = 8.51 min8.51 min

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

represents the mass flow represents the mass flow raterate

The equation for mass flow The equation for mass flow rate = rate = change in mass/timechange in mass/time

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

Mfr = mass / timeMfr = mass / time Mfr = 7000 grams / 7 minMfr = 7000 grams / 7 min Mfr = Mfr = 1000 grams/min1000 grams/min

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

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

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

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

Flow Meter DemoFlow Meter Demo

Volume flow rate equation Volume flow rate equation using speed = using speed = area x speedarea x speed

Mass flow rate equation Mass flow rate equation using speed = using speed = density x density x area x speedarea x speed

To find cross sectional area To find cross sectional area of a pipe use this equation = of a pipe use this equation = pi x rpi x r22

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

A = pi x rA = pi x r22

r = d/2 = 18/2 = 9 mr = d/2 = 18/2 = 9 m A = 3.14 x 9A = 3.14 x 92 2 = 254.34 m= 254.34 m22

Vfr = Area x speedVfr = Area x speed Vfr = 254.34 mVfr = 254.34 m22 x 24 m/s x 24 m/s Vfr = Vfr = 6104.16 m6104.16 m33/s/s

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

A = pi x rA = pi x r22

r = d/2 = 10/2 = 5 mr = d/2 = 10/2 = 5 m A = 3.14 x 5A = 3.14 x 52 2 = 78.5 m= 78.5 m22

Vfr = Area x speed x densityVfr = Area x speed x density Vfr = 78.5 mVfr = 78.5 m22 x 190 m/s x .5 g/L x 190 m/s x .5 g/L Vfr = Vfr = 7457.50 g/s7457.50 g/s