Oil is flowing through a pipe that increases in height by 20 ft as shown in the

Question

Oil is flowing through a pipe that increases in height by 20 ft as shown in the following figure: Ignore head loss and find the following: What is the flow rate, Q at pt A? What is the flow rate, Q at pt B? What is the flow rate, Q at pt C? The area of the pipe at point C is 6 in2, the area at point A is 3 in^2. What is the fluid speed at point C? What is the fluid speed at point A? As shown the pressure at the right end of the pipe is 0 psig. What is the pressure in appropriate psig or psia at point C? Take gamma_oil=0.0325 lb/in^3 or 56.2 lb/ft^3

Explanation / Answer

a) Flow rate at A = Q
Flow rate in the whole pipe = rho*A*V ( at any point)
As the flow rate remains constant through out the pipe, due to continuity equation
Flow rate at A = 3 gpm
b) FLow rate at B = 3 gpm
c) FLow ratre at C = 3 gpm
d) A*V = 3 gpm [ this is folume flow rate and not mass flow rate]
A = 6 in ^2
V = ?
V = 3 gallon per minute / 6 in^2 = 11.3562*10^-3 m^3 /2* 60 second * 0.00193 m^2
V = 0.098067/2 m/s = 1.2454 in/s
e) From continuity equation
A1V1 = A2V2
A*V = 3 gpm [ this is folume flow rate and not mass flow rate]
A = 3 in ^2
V = ?
V = 3 gallon per minute / 3 in^2 = 11.3562*10^-3 m^3 / 60 second * 0.00193 m^2
V = 0.098067 m/s = 2.4909018 in/s

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