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Shutoff Head of a Centrifugal Pump
As early as the 15th century, Daniel Bernoulli noted that the combination of head and velocity was a constant throughout a piping system with incompressible flow.
where V is the velocity of the liquid at the impeller's outer diameter and g is 32.2 ft/s2.
If you're using the English system for measurements, this equation can be simplified into some very nice field rules. These rules are taught in The McNally Institute's pump seminars.
First, we'll examine the velocity term:
where is the impeller diameter, rpm is the speed of the impeller's outer diameter, there are 12 inches/foot and 60 seconds/minute. Now, for rpm = 1750,
At 1750 rpm, the shutoff head is 90% of the impeller diameter squared
This can be rounded to 100% for practical purposes. Looking at most manufacturer's pump curves will show that the shutoff head is between 90% and 110% of the impeller diameter squared at 1750 rpm. At 3500 rpm, the same procedure yields a shutoff head of 3.6 d2 or almost 4 d2 in English units. In the metric system, if you perform a similar analysis using decimeters as your units of measure, you can obtain good results.
So how is this information used? You can use this information to see if a pump is operating near its BEP (Best Efficiency Point). Let's say that a pump discharge gage reads 120 psi while the suction gage reads 20 psi. The pump is pumping at 100 psi. At its BEP, the pump should be between 80-85% of its shutoff head. 100 psi is 83% of 120 psi. The pressure to head conversion is:
Assuming the pump has a 8.5 in diameter impeller and is running at 3500 rpm:
Head = (8.5)2 x 4 = 288 ft (close!)