Question

A fluidic storage tank has a square cross-section (3m x 3m) and a height of 10m. The tank is half-filled with a fluid with the density of 200kg/m3. The tank suddenly develops a leak. A sensor inside the tank instantaneously alerts the owner that the height of the fluid in the tank is decreasing by 1mm/min. Find the flow rate out of the tank at that moment in time.

Answer 1

	Inputs
1)	Storage tank cross-section = 3 m x 3 m
2)	Height of tank = 10 m
3)	Fluid density = 200 Kg/m33
4)	Tank is half filled
	means Height of fluid in Tank = 5 m
5)	sensor reading for loss of fluid height = 1 mm/min ar given instant
	To find flow rate at that moment in time
	Ans --
	Tank cross section = 3 x 3 = 9 m2
	Tank volume = 9 m2 x 10 m = 90 m3
	Actual fluid volume = 9 m^2 x 5 m = 45 m3
	Given is loss of height = 1 mm/min=0.001 m/min
	hence reduction in fluid volume
	'= 0.001 x 3 x 3 = 0.009 m3/min
	We can claim that
	Flow rate out at a time = Reduction in Fluid volume
	Hence flow rate at given time = 0.009 m3 /min
	converting into lit
	1 m3 =1000 lit
	0.009 m3 = 0.009 x1000 = 9 lit /min
	If anybody is intrested in fluid mass out of tank
	then   Mass out per min = density x volume out per min
	'   = 200 x 0.009 =1.8 Kg / min
	Thus flow rate out of tank at that moment = 9 lit /min
	mass of fluid out of tanl at that moment = 1.8 Kg/min