How Does Impeller Tip Speed Relate to The Pump’s Head?

Previously we have discussed tip speed at some length, but to refresh you tip speed is simply the distance that any selected point on the peripheral of the impeller travels in a set time. In other words the “speed” of that point. To calculate tip speed you simply multiply the diameter of the impeller by pi (3.14159) which gives you the circumference of the impeller at the outermost tip.   You then multiply by the rotational speed of the impeller  (usually rpm, or rps) and this result is tip speed. The units for tip speed depend on the type of linear units and time units used, but when applied to impellers the common units are feet/min or meters/ sec.

Having covered that, let’s look at how tip speed affects the pump’s head output.

Those of us who suffered through physics in high school may remember the formula F = ma or force is equal to mass times acceleration. ( For everyone else, my congrats for avoiding hours of painful studying)  This formula can also be applied to centrifugal pumps.

Assuming that the mass of any given liquid passing through a pump will not change, the force ( pressure ) created will be solely as a result of the acceleration.

When an impeller rotates within a centrifugal pump, the vanes accelerate the liquid down the vane providing the liquid mass with a velocity.   The longer the vane (the radial distance from the beginning of the vane at the eye, to the outer end of the vane tip) and the faster the rotational speed, the more acceleration takes place producing a higher exit velocity of the liquid.

Again for those physics people, rotational acceleration = velocity squared / radius

Relating that back to a force (pressure) the illustration to the left shows how

Since velocity equals radius times rotational speed we can substitute these two factors in place of velocity in the original force formula to create the formula below.

F = M * R * 6.283 x 6.283 * n * n

F = M * R * 39.48 * n * n

Substituting diameter for the radius at R = 0.5D  we then arrive at the,

F = M * D * 19.74 * n * n

Going back to our earlier statement that, for any given liquid passing through a pump the mass will not change,  we can see that the only two factors that change to alter the force (pressure) are rotational speed and diameter.

These are the same two factors that give us tip speed. While not exactly a direct relationship it does show that increasing tip speed increases head and that it can be done by either a rotational speed increase or a impeller diameter increase.

I am sometimes asked if it is possible to estimate a pump’s head output when performance data or curves are not readily available, and the answer is yes. There is an old trick that will get you close to the rated head output.  If you take the impeller diameter in inches and square that number, the result will be a close estimate of the pump’s shut-off head in feet when run at 1750 rpm.

The estimate can be refined somewhat if you know the market the pump was designed for. High-efficiency water pumps use 1.1 times the impeller diameter and heavy slurry pumps use 0.9 times the impeller diameter.

For example,  we can use a Toyo DP-10 operating at 1750 rpm as a test case. Knowing it is a heavy-duty slurry pump, we would multiply the impeller diameter of 9.53 inches by 0.9 to obtain 8.58, squaring that number we obtain 73.5. A DP-10 has a shut-off point of approximately 70 ft, thus verifying our estimating formula .

 Note. For pump speeds other than 1750 rpm, use affinity laws to compensate accordingly.

Cheers

RJ