Calculate the volumetric flowrate (Q, m3
/s) of a pump whose power output is 0.75 hp
and efficiency of 65%, producing a differential pressure of 120 Pa. Equation is shown below:
Q =
Pη
∆P
Where:
P = power output in Watts (W)
η = efficiency
ΔP = differential pressure in Pa

To calculate the volumetric flow rate (\(Q\)) of the pump, we'll use the given formula:

\[
Q = \frac{P \cdot \eta}{\Delta P}
\]

Where:
- \(P\) = power output (in watts, W),
- \(\eta\) = efficiency (as a decimal),
- \(\Delta P\) = differential pressure (in pascals, Pa).

### Given values:
- Power output (\(P\)) = 0.75 hp,
- Efficiency (\(\eta\)) = 65% = 0.65,
- Differential pressure (\(\Delta P\)) = 120 Pa.

First, we need to convert the power from horsepower (hp) to watts (W). The conversion factor is:

\[
1 \, \text{hp} = 745.7 \, \text{W}
\]

So:

\[
P = 0.75 \, \text{hp} \times 745.7 \, \text{W/hp} = 559.275 \, \text{W}
\]

Now, we can calculate the volumetric flow rate \(Q\):

\[
Q = \frac{P \cdot \eta}{\Delta P} = \frac{559.275 \, \text{W} \times 0.65}{120 \, \text{Pa}}
\]

Let's compute that.The volumetric flow rate (\(Q\)) of the pump is approximately \(3.03 \, \text{m}^3/\text{s}\).

Would you like further details or explanations on this calculation?

Here are five related questions:
1. How does pump efficiency affect the volumetric flow rate?
2. How can power losses impact the overall performance of the pump?
3. What is the significance of differential pressure in a pump system?
4. How would the flow rate change if the efficiency of the pump were higher?
5. What happens to the volumetric flow rate if the differential pressure increases?

**Tip:** Always check the units during calculations, as incorrect conversions can lead to significant errors.

Calculate the volumetric flowrate (Q, m^3/s) of a pump whose power output is 0.75 hp and efficiency of 65%, producing a differential pressure of 120 Pa.

Learn how to calculate the volumetric flowrate of a pump with a power output of 0.75 hp, 65% efficiency, and a differential pressure of 120 Pa using the formula Q = (P * η) / ΔP. Includes a step-by-step guide for unit conversion and application in fluid dynamics.

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