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# Working with flow rate

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A rectangular open tank is 4.5' wide, 3' deep and 6' long. We wish to fill the tank using a 1" diameter hose that delivers water at a speed of 100 inch/s. a) Determine the volume of the tank in gallons and liters. b) Compute the volume of water delivered by the hose in bothe quarts and liters per second. c) How long will it take to fill up the tank?

https://brainmass.com/physics/mathematical-physics/working-flow-rate-33753

## SOLUTION This solution is FREE courtesy of BrainMass!

Volume = length * height * breadth

But here the units are in inches so we have to convert them to a standard unit first.

we know that 1 inch = 0.0254 meters

So the dimensions of the tank are,

4.5*0.0254 = 0.1143 m wide
3 * 0.0254 = 0.0762 m deep
6 * 0.0254 = 0.1524 m long

===> the volume = 0.1143 * 0.0762 * 0.1524 = 0.001327352184 m^3

Also 1 liter = 10^-3 meters^3

== > 0.001327352184 m^3 = 0.001327352184 m^3 *10^3 = 1.327352184 liters ---Answer

Again 1 liter = 0.264172051 US gallon

==> 1.327352184 liters = 1.327352184 * 0.264172051 = 0.350 Gallon --- Answer

Crosssectional area of the pipe

= pi*R^2 = 3.14 * 0.5" = 3.14 * (0.0127)^2 = 0.0005064506 meter^2

Rate of pumping = 100inch/sec = 2.54meter/sec

Volume pumped in per second

= 0.0005064506 meter^2 * 2.54meter/sec

= 0.001286384524 meter^3 / second

1 quarts = 0.9463 liters ==> 1liter = 1.0566882 US quarts

Now, the pumping rate = 1.29*1.0566882 US quarts/sec = 1.36 quarts/sec --Answer

Volume = 0.001327352184 m^3
Pumping rate = 0.001286384524 meter^3 / second

thus the time required to fill the tank = 0.001327352184 m^3/0.001286384524 meter^3 / second