A centrifugal pump impeller has an outside diameter of 290mm and the with at the outlet is 110mm. The vanes are set back at an angle of 35 degrees to the tangent to the impeller at the vane tip. The diameter of the suction and delivery pipes is 290mm. Gauges at points on the delivery and suction pipes close to the pump and each 1.5m above the sump level showed heads of 18.6m above and 3.4m below atmosphere respectively while the pump was delivering 180 l/s at a speed of 1200 rev/min. It requires 68kW to drive the pump. Assume the water enters the impeller radially and without shock. Calculate the overall efficiency, manometric efficiency Abe the pressure head loss in the suction pipe

To calculate the overall efficiency and manometric efficiency of the centrifugal pump, as well as the pressure head loss in the suction pipe, you will need to follow these steps:

1. Calculate the total head (H) developed by the pump. The total head is given by the equation: H = (HQ + HM), where HQ is the pressure head and HM is the velocity head. Since the water enters the impeller radially and without shock, the velocity head is zero. Therefore, H = HQ.

2. Calculate the pressure head (HQ) by subtracting the suction head (H1) from the delivery head (H2). H2 = 18.6 m (above atmosphere) and H1 = -3.4 m (below atmosphere). So, HQ = H2 - H1 = 18.6 - (-3.4) = 22 m.

3. Calculate the power input (Pin) to the pump using the formula: Pin = (Q * H)/367, where Q is the flow rate in m^3/s and H is the total head in meters. Convert the flow rate from liters per second (l/s) to cubic meters per second (m^3/s): Q = 180 l/s * 0.001 = 0.18 m^3/s. Substitute the values: Pin = (0.18 * 22)/367 = 0.0108 MW.

4. Calculate the overall efficiency (η) of the pump using the formula: η = (Pout/Pin) * 100, where Pout is the output power from the pump. Convert the power input from MW to kW: Pin = 0.0108 MW * 1000 = 10.8 kW. Pout is given as 68 kW. Substitute the values: η = (68/10.8) * 100 = 629.6%.

5. Calculate the manometric efficiency (Abe) of the pump using the formula: Abe = (HQ*Q)/(Pin*9.81), where 9.81 is the acceleration due to gravity in m/s^2. Substitute the values: Abe = (22 * 0.18)/(10.8 * 9.81) = 0.035.

6. Calculate the pressure head loss in the suction pipe using the D'Arcy-Weisbach equation: H_loss = (f * (L/D) * (V^2))/(2 * g), where f is the D'Arcy-Weisbach friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the average velocity, and g is the acceleration due to gravity. Since the water enters the impeller radially and without shock, the average velocity is zero. Therefore, the pressure head loss in the suction pipe is zero.

In summary:
- Overall efficiency (η) = 629.6%
- Manometric efficiency (Abe) = 0.035
- Pressure head loss in the suction pipe = 0

Note: To obtain more accurate results, it may be necessary to use additional information such as pump curves, efficiency curves, and fluid properties.