Centrifugal Pumps: Differential Head (∆H) Vs. Pressure (∆P)

In the world of fluid mechanics, there is a common point of friction between Pump Manufacturers (who talk in "Head") and Plant Operators (who talk in "Pressure"). Understanding the distinction is vital for troubleshooting, pump selection, and equipment safety. 

A centrifugal pump is a constant head machine. This means that at a given RPM and flow rate, the pump will lift any liquid to the same height, regardless of its weight or density. 

Before going into discussion of differential head vs differential pressure in centrifugal pump we must know what does differential head (Total head) means for centrifugal pump.

We can specify differential head in various terminology.

Some of terminologies are:

·       Total work done on the fluid by the pump

·       Discharge vessel (Liquid level) elevation minus the suction vessel elevation (Liquid Level)

·       Discharge Head – Suction Head

·       Parameter which measures the pump’s ability to develop a specified discharge pressure

·       Discharge head plus the suction lift

·     Differential reading of pressure gauges which are installed on discharge side of the pump and the suction side of the pump

·       Parameter which measures the pump’s ability to raise the liquid to a specified height

Suction Head : It is the available head at the suction nozzle of the pump.

Discharge Head : It the vertical distance between the center line of the pump and the liquid level in the discharge vessel. Also referred as suction head plus the differential head developed by the pump.

Suction Lift : It is the difference between the pump center line elevation minus the suction vessel liquid level. It is applicable particularly when the liquid level in the suction vessel is below the center line of the pump. Also known as the negative suction head.

Figure 1: Differential Head

 

Differential head Vs Differential Pressure

             

Figure 2: Differential Head Vs Differential Pressure

 

Above figure 2 shows three identical pump which has the same differential which are used to pump three different liquids having specific gravity of X, Y and Z respectively.

Three pumps develop equal differential head irrespective of the fluid which is to be pumped. But the differential pressure developed by the pump varies with respect to change in the specific gravity of the fluid. Higher the specific gravity higher the differential pressure.

 

Figure 3: Differential Head Vs Differential Pressure

 

Above figure 3 shows three pumps (non identical) which develops the same differential pressure which are used to pump three different liquids having specific gravity of X, Y and Z respectively.

These three pumps develop same differential pressure. In this case these pumps develop different differential head. Differential head developed by the pump varies with respect to the specific gravity of the fluid which is to be pumped, Higher the specific gravity lower the differential head.

This concept of differential pressure and differential head creates confusion between the maintenance engineer who is working in the plant and the pump manufacturer. Maintenance people always read the pressure gauge reading and record when the pump manufacturer always use the word differential head for dictating the performance of the pump. A pump which is developing the head of 30 for water, the same pump will develop the same head for the concentrated sulfuric, gasoline or any other liquid irrespective of the liquid. Pump manufacturer doesn’t know the ultimate service of the pump when he is manufacturing pump. The pressure reading of the pressure gauges is function of the specific gravity. This the reason why we do not specify the pump by the differential pressure. If the maintenance engineer or the person wants to have a conversation with the manufacturer then, he must understand the concept of “Head”. This is the reason why the most of the pump sold without adequate gauges.

Formulas to convert differential head to differential pressure.

 

 

Example: A centrifugal pump which is capable of developing the differential head of 50 m (164 ft) at 10 m3/hr flowrate. Calculate differential pressure developed by the pump for the following mentioned fluids.

1.     Water having specific gravity of 1.0

2.     Benzene having specific gravity of 0.87

3.     Gasoline having specific gravity of 0.75

4.     Concentrated nitric acid having specific gravity of 1.5

5.     Concentrated sulfuric acid having specific gravity of 1.8

Answer: Differential pressure developed by the pump at 10 m3/hr flowrate is calculated below:

1.     Water having specific gravity of 1.0

·       Differential Pressure (psi) = Differential Head (ft) X Sp.gr. / 2.31

                                                                  = 164 X 1 / 2.31

                                                                  = 71 psi

·       Differential Pressure (kg/cm2) = Differential Head (m) X Sp.gr. / 10

                                                                          = 50 X 1 / 10

                                                                          = 5 kg/cm2

·       Differential Pressure (bar) = Differential Head (m) X Sp.gr. / 10.20

                                                                   = 50 X 1 / 10.20

                                                                   = 4.9 bar

 

2.     Benzene having specific gravity of 0.87

·       Differential Pressure (psi) = Differential Head (ft) X Sp.gr. / 2.31

                                                                  = 164 X 0.87 / 2.31

                                                                  = 61.8 psi

·       Differential Pressure (kg/cm2) = Differential Head (m) X Sp.gr. / 10

                                                                          = 50 X 0.87 / 10

                                                                          = 4.35 kg/cm2

·       Differential Pressure (bar) = Differential Head (m) X Sp.gr. / 10.20

                                                                   = 50 X 0.87 / 10.20

                                                                   = 4.3 bar

 

3.     Gasoline having specific gravity of 0.75

 ·       Differential Pressure (psi) = Differential Head (ft) X Sp.gr. / 2.31

                                                                     = 164 X 0.75 / 2.31

                                                                     = 53.24 psi

·       Differential Pressure (kg/cm2) = Differential Head (m) X Sp.gr. / 10

                                                                          = 50 X 0.75 / 10

                                                                          = 3.75 kg/cm2

·       Differential Pressure (bar) = Differential Head (m) X Sp.gr. / 10.20

                                                                   = 50 X 0.75 / 10.20

                                                                   = 3.67 bar

 

4.     Concentrated nitric acid having specific gravity of 1.5

·       Differential Pressure (psi) = Differential Head (ft) X Sp.gr. / 2.31

                                                                  = 164 X 1.5 / 2.31

                                                                  = 106.5 psi

·       Differential Pressure (kg/cm2) = Differential Head (m) X Sp.gr. / 10

                                                                          = 50 X 1.5 / 10

                                                                          = 7.5 kg/cm2

·       Differential Pressure (bar) = Differential Head (m) X Sp.gr. / 10.20

                                                                   = 50 X 1.5 / 10.20

                                                                   = 7.35 bar

 

5.     Concentrated sulfuric acid having specific gravity of 1.8

·       Differential Pressure (psi) = Differential Head (ft) X Sp.gr. / 2.31

                                                                  = 164 X 1.8 / 2.31

                                                                  = 127.8 psi

·       Differential Pressure (kg/cm2) = Differential Head (m) X Sp.gr. / 10

                                                                          = 50 X 1.8 / 10

                                                                          = 9 kg/cm2

·       Differential Pressure (bar) = Differential Head (m) X Sp.gr. / 10.20

                                                             = 50 X 1.8 / 10.20

                                                             = 8.8 bar

The Hidden Variable: Power Requirement

While the Head remains the same, the Brake Horsepower (BHP) required to move the fluid increases linearly with Specific Gravity.

 

 

Maintenance Tip: If you switch a pump from Water to Sulfuric Acid, the pressure gauge will go up, but so will the Amperage on the motor. Failure to account for the higher Sp.Gr can result in a tripped breaker or a burnt-out motor.

Conclusion

A pump manufacturer specifies "Head" because they do not know what fluid you will eventually pump. As a maintenance engineer, you must always convert your gauge readings (P) to Head (H) using the fluid's Specific Gravity before comparing your pump's performance against the manufacturer’s original test curve.