The required water flow rate in the 6 cm diameter 30 meter long circular pipe in the diagram above is 12 liters per second. The water temperature is 4 °C and the flow discharges into the atmosphere at a pressure of PB = 100 kPa. The flow is fully developed turbulent flow and there is no elevation change. The surface of the wall has become degraded due to pitting and deposits such that there is a surface roughness with a height of 0.5 mm. Find the following: a) The mean flow velocity in the pipe. b) The Reynolds number. c) The Darcy friction factor, ?. d) The pressure at the pump exit location, PA, required to achieve the specified flow rate

Problem 1: The required water flow rate in the 6 cm diameter 30 meter long circular pipe in the diagram
above is 12 liters per second. The water temperature is 4 °C and the flow discharges into the atmosphere
at a pressure of PB = 100 kPa. The flow is fully developed turbulent flow and there is no elevation change.
The surface of the wall has become degraded due to pitting and deposits such that there is a surface
roughness with a height of 0.5 mm. Find the following:
a) The mean flow velocity in the pipe.
b) The Reynolds number.
c) The Darcy friction factor, ?.
d) The pressure at the pump exit location, PA, required to achieve the specified flow rate.

Problem 2: For the system described in Problem 1, calculate the pumping power required to produce
the pressure PA at the specified flow rate. The pressure at the pump inlet is 105 kPa and the velocity at
the pump inlet can be taken to be negligible (Vinlet=0).