Exercise: Determining efficiency and brake horsepower

In this module the main ways to find the efficiency will usually be through the pump curves or the given efficiency equation:

$η = (\frac{W_{s}}{W b h p})$

In this equation eta (η) is the efficiency that we are wanting to find, and W_s is the shaft work while Wbhp is the other one we want to find or the brake horsepower.

Using the following pump curve there is a provided question. The pump curve used is the Shipco Pumps, type 132, Model D, 1750 RPM. (I did not have permission to upload an image)

EX: A pumping system with water is designed to have a flow rate of 500 GPM against a head of 40 feet using a Schipco Type 132 Model D (1750 RPM) pump. The pump curve is stated above, find the pump efficiency and the brake horsepower.

To find the efficiency, looking at the graph, the y axis has the head feet, while the x-axis has the flow rate in GPM. Since we were given 500GPM and a head of 40 ft, by looking at the graph it lands at the point between the curves labeled 70% and 65%. Since it is closer to the 65% curve it is good to assume that the pump efficiency is roughly 66%.

To find the brake horsepower the shaft work of the liquid would need to be known. To find that we need the following equation:

$W_{s} = V * ρ * g * H$

The V is flow rate which is given to us as 500 GPM, rho (ρ) density can be found using engineering toolbox to be 8.34 (lbm/gal), g the gravity is 32.174 (ft/s^2) and H the head is also given to us as 40 feet.

Putting all this together we get the shaft work to be 5.05 hp.

Using the shaft work and the found efficiency we can find the brake horsepower using the 1st equation to get the brake horsepower of 7.65 hp.