Question

Consider the flow of water through the circuit shown in the figure, moving water from reservoir A to reservoir B. The pipe is made of copper tubing with an inside diameter of 12 mm. For water take p = 1000 and v = 1.14 x 10-6 m2 Assume that a = 1 everywhere. Elevation m Reservoir B Elevation Z1 = 1 m Pipe entrance r/d=0 90° smooth bends, r/d=1 Angle valve wide open V Reservoir A ID = 12 mm, total pipe length 20 m Pump=0.85 a) (30%) Assuming that the flow rate is Q = 3 x 10-3m" -3 ", calculate the friction factor in the pipe and the power required by the pump; the pump has an overall efficiency Tipump = 0.85. f = Wpump = W b) (30%) The power to the pump is now changed to 15kW. Assuming the same efficiency for the pump, what will be the new flow rate? Show the iterations. Alternatively, if you prefer to work in Excel, list here your result and attach the Excel file with your calculations. Q = "It
minimum of 3 significant figures please

Answer 1

The equation balancing the heads is written. From the given flow rate and the diameter of pipe, the velocity of the flow is calculated. Once velocity is known, the Reynolds Number is calculated after that. The Prandtl Relation for smooth wall is used to calculate the friction factor. This equation is solved iteratively by guessing an intial solution and repeating by different values till convergence is acheived. Once friction factor is known, the friction head loss is calculated. For the given r/d at entrance and bending, the loss coefficient is taken from the manual. The head loss due to bend and entrance is then obtained. Finally, these calculated head losses are substituted back into the equation balancing the head and head by pump is then calculated. Once head by pump is obtained, power required by pump can be calculated.

If the pump work (power) is changed, the flow rate and the head generated by pump will change. Since the flow rate will change, the flow velocity will change and thus Reynolds Number will change and subsequently friction factor will change. Thus we will have three equations with three unknowns, friction factor (f), velocity of flow (v) and the head of pump (H). Since these equation are not explicit in nature and thus cannot be linearly seperated, they are solved by guessing the solution and then updating the values till the convergence is achieved.