Question

A glycerin pump is powered by a \(5-\mathrm{kW}\) electric motor. The pressure differential between the outlet and the inlet of the pump at full load is measured to be 211 kPa. If the flow rate through the pump is \(18 \mathrm{L} / \mathrm{s}\) and the changes in elevation and the flow velocity across the pump are negligible, the overall efficiency of the pump is \((a) 69\) percent \((b) 72\) percent \((c) 76\) percent \((d) 79\) percent \((e) 82\) percent

Short answer

Answer: (c) 76%

Step-by-step solution

Convert flow rate from L/s to m³/s

First, we need to convert the given flow rate from L/s to m³/s for the calculations. We know that 1 L = 0.001 m³, so we can convert the flow rate as follows: Flow rate (m³/s) = 18 L/s × 0.001 m³/L = 0.018 m³/s

Convert pressure differential from kPa to Pa

Next, we need to convert the given pressure differential from kPa to Pa for the calculations. We know that 1 kPa = 1000 Pa, so we can convert the pressure differential as follows: Pressure differential (Pa) = 211 kPa × 1000 Pa/kPa = 211000 Pa

Calculate hydraulic power

Now that we have the flow rate (0.018 m³/s) and pressure differential (211000 Pa) in the correct units, we can calculate the hydraulic power using the formula mentioned in our analysis: Hydraulic Power (W) = Flow rate (m³/s) × Pressure differential (Pa) Hydraulic Power (W) = 0.018 m³/s × 211000 Pa = 3798 W

Convert hydraulic power from W to kW

To make it compatible with the given power supplied (5 kW), let's convert the hydraulic power from watts (W) to kilowatts (kW). Hydraulic Power (kW) = 3798 W × 0.001 kW/W = 3.798 kW

Calculate the pump efficiency

To find the overall efficiency of the pump, we'll divide the calculated hydraulic power (3.798 kW) by the power supplied to the motor (5 kW) and multiply the result by 100 to get the percentage. Pump Efficiency (%) = (Hydraulic Power / Power supplied) × 100 Pump Efficiency (%) = (3.798 kW / 5 kW) × 100 = 75.96 % The pump efficiency is approximately 76 % (rounded to the nearest whole number). So, the correct answer is: \((c) 76\) percent