A venturi-type obstruction flow meter is used to monitor flow rates through a 1.
ID: 2995628 • Letter: A
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