Water enters a boiler through a tube with a 130 mm inner dia

Water enters a boiler through a tube with a 130 mm inner diameter at 6 MPa and 65 degreeC, and leaves the tube at 5 MPa and 450 degreeC with a velocity of 80 m/s Find: the velocity of the water at the tube Inlet and the volume flow rate at the inlet.

Solution

density of water at 65 C is rho1 = 981.3 kg/m^3

density of water at 450 C is rho2 = 601.6 kg/m^3

by using Bernoullies theorem

P1+(0.5*rho1*v1^2) = P2+(0.5*rho2*v2^2)

(6*10^6)+(0.5*981.3*v1^2) = (5*10^6)+(0.5*601.6*80^2)

v1 = 43.42 m/s is the answer for a)

b) volume flow rate is A1*v1= 3.142*(130/2)^2*10^-6*43.42 = 0.576 m^3/sec