# Determining flowrate (GPM) through a partially open gate valve

1. Oct 21, 2011

### Sixdirty6

Hello all, trying to figure this out. I work at a shipyard and operate/maintain the drydock. The discharge tunnel that flows water out into the ocean has culverts about 24.5' x 15.5' x 8'. Connected to the bottom of the culvert is a 48" pipe that goes to a gate valve of the same diameter. If I were to drain a culvert full of sea water into a lower chamber, what would be the flow rate (in GPM) if the valve were @ 100% open and @ 10% open?

Thanks for looking!

2. Oct 21, 2011

### edgepflow

You may apply the following formula (Ref: Crane Technical Paper 410, 25th Printing, Equation 2-7):

Q = 7.9 $C_{v}$ $\sqrt{\Delta P / \rho}$

where,

Q = flow rate in gpm
Cv = flow coefficient in gpm/psi
ΔP = pressure difference in psi = $\rho$ g h for non-pumped elevation difference
$\rho$ = fluid density in lb/ft^3 = 62.2 lb/ft^3 for ambient water
h = elevation difference between flowing sections

Note there are about 0.433 psi per foot of water column.

The Cv may be provided by the valve manufacturer. If you can find, let me know. I can help you estimate.

Last edited: Oct 21, 2011
3. Oct 24, 2011

### Sixdirty6

Thanks for replying! I can't seem to find the Cv for this particular valve (Crane 54" cast iron gate valve). Is there a formula to calculate Cv from the specifications of the valve?

4. Oct 24, 2011

### edgepflow

We can estimate from Crane Technical Paper 410. I have this at work. Will get back to you!

5. Oct 25, 2011

### edgepflow

From Crane Technical Paper 410, 25th Printing, Appendix A, we will estimate Cv for the full open gate valve. The form loss factor is:

$K_{1}$ = 8 $f_{T}$

where,

$f_{T}$ = Darcy friction factor = 0.012 for 48" pipe in turbulent flow

And now,

$C_{v}$ = 29.9 $d^{2}$ / $\sqrt{K_{1}}$

Where d is the pipe ID in inches.

Try this, and see what you get. Then we can include the entrance and exit effects, straight pipe (if any) and the 10% open gate valve.