What is the flow rate of water through this pipe?

Question

I have a standard 55 gal drum: 35" tall and 24" wide. At the bottom of the drum at one side is a 1" diameter PVC pipe used to drain water. If the drum is full: what is the flow rate (GMP) of the water moving through the PVC pipe?

Is there an equation I can use to find this flow rate at different volumes? For eaxample: if the drum is 1/2 full, 1/4 full, etc.

Thank you!

Answer 1

 

ρ g h=½ ρ v²   (from Bernoulli equation or you can think of it as potential energy changing to kinetic energy) 

 

so

 

v=sqrt( 2gh)

 

 

v=sqrt(2 x 32ft/s² x 35in) = sqrt (2 x 32ft/s² x (35/12)ft)=186.7ft/s

 

Q=vA

 

A=πr²=π (0.5)²=0.785 in²=0.785/(12x12)=0.785/144=5.45x10-³  ft²

 

Q=186.7 x 5.45x10-3=1.02 ft³/s

 

since 1ft³=7.47 gal and 1min is 60 s

 

Q=1.02 ft³/s x(7.47) x60= 457 gal/min

 

if you want a formula Q=vA= sqrt(2gh) x A

 

for half full h is half and for 1/4 full h is 1/4 (35/2 0r 35/4) but then you have to be careful with the units

 

best

shirin