A venturi-type obstruction flow meter is used to monitor flow rates through a 1.

Question

A venturi-type obstruction flow meter is used to monitor flow rates through a 1.50 inch water supply line in a processing facility. Periodic maintenance on facility components is scheduled to be performed after 100,000 gallons of water has passed through the system. If a constant differential pressure ?P = 1.0 psi is maintained across the meter, how much time will elapse between maintenance events?

DATA:

Water density ?water = 62.4 lbm/ft3  

Nozzle major diameter D= 1.50 inch, throat diameter d = 1.00 inch     

Discharge coefficient Cnozzle=0.98

1 gallon = 231 in3

   1 foot = 12 inches

   gc = 32.2 (ft*lbm)/(lbf*s2)

lbm = pounds, mass

lbf = pounds, force

Explanation / Answer

Flow rate Q = Cd*A_throat*sqrt [2*g*(dP / rho) / (1 - (A_throat / A_main)^2)]
= 0.98*(3.14/4 *(1/12)^2)*sqrt [2*32.2*(1*12^2 /62.4) / (1 - ((1 / 1.5)^2)^2)]
= 0.0727 ft^3/s
= 0.0727*12^3 / 231 gallon / s
= 0.54385 gallon/s

To flow 100,000 gallons, time required = 100,000 / 0.54385 = 183872.7 s
= 2 days 3 hours 4 min 32.7 s

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