Answer Happy

Pasteurised milk, which is being held in tank at a constant height of 3.5 m from the floor, is transported into a vat where it is dispensed into sterile cartons to be sent to supermarkets. The milk is pumped from the tank along 100 m total of straight smooth pipes of diameter 47.47 mm, which along the way, contains 2 90° elbow joints to navigate around other machinery in the factory, and 2 similar 90° elbow joints to raise the pipeline level to the top of the vat, which is 19 m above the floor. The pipeline system also contains an angle valve to control the flow between the tank and the vat. If the pasteurised milk, which has a viscosity of 0.001 Pa, s and density of 1000 kg/m³, is being pumped at an average velocity of 1.9 m/s through the pipelines, calculate the following: The Reynolds number of the flow: The energy loss, in J/kg, of the 2 elbow joints if they each have a friction loss coefficient of 1.5: J/kg The energy loss, in J/kg, of the valve if it has a friction loss coefficient of 2 J/kg The major friction losses, in J/kg, along the 100 m of pipe, given that the friction factor is 0.0046 (you can check this for yourself on the Moody chart - treat it as practice!): J/kg The energy loss, in J/kg due to sudden contraction from the tank to the pipeline (note: the height of the tank is significantly larger than the diameter of the pipeline): J/kg Hence, the total energy loss due to friction: J/kg The total energy requirement of the pipe, in J/kg: J/kg Based on a velocity of 1.9 m/s and a diameter of 47.47 mm, the mass flowrate of the milk is 3.36 kg/s (you can check this calculation for yourself!). Calculate the total energy requirement of the pump, assuming an efficiency of 100%: W