After diving into the history and basic principles of industrial pumps, after having applied the Bernoulli equations to explain the functioning of centrifugal pumps, after building a tiny version of a water pump with recycled materials, in this video we are going to learn pump calculations and in the specific we’re going to learn how to calculate:
the FLOW RATE, the revolutions per minute RPM, the HEAD PRESSURE, the PUMP POWER and the IMPELLER DIAMETER.
If you have already installed a centrifugal pump you should have a datasheet like this one, a datasheet is essentially a document that summarizes the performance and the other technical data of your pump.
Unfortunately, very often some technical data are missing from these data sheets, but despite this, some formulas can be used to calculate and obtain these missing data.
We will also see what happens if we try to modify some of these parameters.
Of course, if you have not yet installed the pump or you are still in the development phase, you can also use these formulas to determine what will be the performance of your pump.
It is good to remember that these calculations will only provide us with theoretical values.
The actual performance of the pump could in fact be slightly difference compared to these results.
And of course an older pump will have a greater discrepancy between the theoretical and the practical, so it may be necessary to add a correction factor.
As we have already seen in our previous video about the functioning of centrifugal pumps, the basic principle of these type of pumps is to transform volumes of fluid from a region of low pressure to a region of high pressure. The atmospheric pressure in fact, pushes the fluid thanks to the vacuum created in the suction pipe allowing the fluid to flow into the delivery pipe.
In these dynamics we can not fail to mention the FLOW RATE, which is the volume of fluid (liters or cubic meters) that can be moved by the pump in a unit of time. Generally the flow rate can be expressed in cubic meters per hour, liters per minute or in liters per second for high flow pumps.
The ROTATIONS PER MINUTE or RPM is instead the number of turns in one minute which is equal to the number of revolutions or cycles completed in one minute by the rotating element of the pump, better known as the impeller, which converts the mechanical energy first into kinetic energy and then into hydrodynamic energy allowing the fluid to flow from the suction pipe into the delivery pipe.
Well, now we are going to find out what would be the NEW FLOW RATE if we had to increase or decrease the RPM of the pump, and to do that we will use this formula, that is the new value of the RPM multiplied by the division of the old flow rate value and the old RPM value.
To solve this equation I’ve separeted the metric and the imperial system to perform the calculations with both measurement (mesiormen) systems. Furthermore, colors will help us to better distinguish different values.
So, if we use these new values, we can see that the pump would originally have a flow rate of 57 liters per second and we can see the modified RPM and the original RPM. In the imperial system side the values are transformed into Gallons per minute.
In the metric system side I will use the liters per second, but you are free to change the values in cubic meters per second or kilograms per second. In any case, following these formulas the result will be 52.6 liters per second or 833.97 gallons per minute.
Now we are going to calculate the value of the NEW FLOW RATE in the case we need to change the diameter of the impeller, which is not very practical since changing the size of the impeller by adding or subtracting material is not the better solution. A good way is to use a frequency converter to change the speed of the pump and keep the design criteria intact, but if you are still trying to actually trim down the impeller diameter, then you need to follow these calculations.
So in this case, the NEW FLOW RATE is equal to the new diameter of the impeller multiplied by the division between the old flow rate and the old impeller diameter. Using these values we will get 52.6 liters per second or 833 gallons per minute.
The next value we are going to calculate is the RPM of the pump.
What RPM we need if we want to increase or decrease the flow rate? The new RPM value is equal to the old RPM value multiply it by the division between the new flow rate value and the original flow rate value. Following the calculations you cancel out the liters per second and find this ratio that multiplied by the original RPM will result in 1300 (thirteen hundred) rpm, which is the rotation speed that the impeller must reach to withstand the new flow rate.
Now let’s move on to the calculation of HEAD PRESSURE. We can simply define the HEAD PRESSURE as the ability of a pump to elevate at a certain height a certain number of cubic meters of fluid.
This value depends on the suction head of the pump, so if the RPM of the pump, is increased or decreased.
So to find out the value of the NEW HEAD PRESSURE if we are going to increase or decrease the RPM, first of all we need to square the value of the new RPM and multiplied it by the division of the old head pressure value and the old RPM value squared as well.
Make sure to square both of these RPMs values. I wrote these numbers not in a standard form to see every single value and get the result of 364 kPa, or 122 feet of water which is the value of the new head pressure.
Now we are going to find out what is the value of the NEW HEAD PRESSURE if we are going to increase or decrease the flow rate and to do that we have to multiply the old head pressure by the division of the new flow rate value and the old flow rate value making sure to squared the number we get from this division.
Squaring the result of this division, we obtain this value, that multiplied by the the old head pressure value, allows us to get 364 kPa, which is the value of the new head pressure.
The next step is to calculate the PUMP POWER. The pump power is the power consumed by the pump in order to move and increase the pressure of a fluid. The power requirement of the pump depends on a number of factors including the pump motor efficiency.
So to calculate what is the NEW POWER if we are going to increase or decrease the RPM of the pump, we have to cube the value of the new RPM and multiply it by the old power value and the old RPM value cubed as well.
Make sure to cube the values of the new and the old RPM and once again I write these numbers not in a standard form to better understand the calculations performed. By multiplying this numbers we can notice that the new power will come down to 35.5 kilowatts compared to the initial 45 kilowatts. In the imperial system side we see that the power will come down from 60.35 horsepower to 47.5 horsepower.
In conclusion we are going to calculate the pump IMPELLER DIAMETER.
How much should the impeller diameter measure if we want to reach this new flow rate level?
This calculation is used in case of the impeller is trimmed down to meet a new flow rate and so is what I’ve done in the calculations, even here we see that originally old flow rate value was 57 liters per second or 903.5 gallons per minute and the new flow rate I want to reach in the metric system of this scheme is 52.6 liters per second or 833.7 gallons per minute.
Also in this case we cancel out the liters per second of this division to find this ratio which we multiply by the old impeller diameter value to find 184.56 mm or 7.26 inches, which is the new measure of the impeller diameter.