[vhpk]

Hi everyone,
I've got a question regarding the energy calculation:
Estimate the power required to pump milk at 20°C at 2.7 m s^-1  through a 4 cm diameter steel tube that is 130 m long, including the kinetic energy and the friction energy. The viscosity of milk at 20⁰C is 2.2x10^-3, density is 1030kg/m³.The roughness for steel is from 0.9mm to 9mm
At first, I calculated the potential and kinetic energy,
E_p =hg= 1275.3(J)
E_k = v²/2 = 3.645(J)
Reynold number = density x velocity x diameter/viscosity = 50563.6 so the flow here is turbulent
The tube here is made of steel, I chose 9mm for the roughness e.
For turbulent flow:
C_f = 0.001375(1+(20000e/d+106/Re)^0.33) = 0.0235
The energy of friction loss:
E_f = 2C_fv²L/D = 1112.6(J)
So the total energy for pumping is :
E = E_p + E_k + E_f = 2391.55J
So the total energy required:
E x mass flow rate = E x velocity x cross sectional area x density = 8380.12Js^-1
The result in textbook is just 297.05J
I'm confused since I don't know where and when I was wrong. Plz help me with this .
Thanks a lot