Help for calculating the pressure anywhere in a pump system


Applets are programs based on the java language that are designed to run on your computer using the Java Run Time environment.


It is possible to calculate the pressure head, which is the specific energy of pressure, anywhere within a system and with the pressure head, the pressure can be calculated. If you know the conditions at the outlet of a system then you can calculate the pressure anywhere upstream of that point all the way to the pump. The same is true if you know the conditions at the inlet of the system, then you can calculate the pressure anywhere downstream of that point all the way up to the pump. This is what this applet does for you.


The outlet of the system is defined as the point where the fluid meets a fixed pressure environment such as the fluid surface of the discharge tank where it meets atmospheric pressure for an open tank. Or if the tank is pressurized, at the point where the fluid surface meets the pressurized environment within the tank. The same reasoning is applied to locate the inlet point of the system in the suction tank.


Determine the pressure anywhere on the discharge side of the pump (see Figure 1 below)

The conditions that must be known at the outlet are:


z2: the elevation of the outlet point of the system with respect to an arbitrary datum plane, if the pipe is open to atmosphere then z2 is the elevation of the pipe end with respect to the datum plane. If the outlet is the surface of the liquid in the discharge tank then z2 is the elevation of fluid particles on the surface with respect to the datum plane. It does not matter where the datum plane is located as long as you use the same one for zx. The pump suction centerline is often used as the level for the datum plane;


zx: the elevation of point X with respect to the datum plane where the pressure is required;


v2: velocity of the fluid at the outlet, if the outlet is the surface of a discharge tank then this velocity is small and close to zero, if the pipe is open to atmosphere than the velocity is the velocity at the pipe end;


H2: the pressure head at the outlet of the system, if the tank is pressurized then H2 is the pressure head corresponding to the pressure in the tank. As an example, say the tank is pressurized at 10 psi then H2 = 2.31 x 5 / SG (SG: specific gravity of the fluid), if the fluid is water then SG = 1 and H2= 11.5 ft.


SG: the specific gravity of the fluid (non-dimensional), water has an SG value of 1.0.


The pipe friction is Hf or HFX-2 in the equation 1.1 below, between the point where the pressure is required, point X, and the outlet must be calculated separtely (this is not done by the applet). You will have to calculate this using the Darcy and Colebrook equations or tables that are available in the Cameron Hydraulic data book, or tables in the Standards book from the Hydraulic Institute.


Lastly, you need to know the equipment friction loss HEQ or HEQX-2 in the equation 1.1 below, for all the equipment between the point where the pressure is required, point X, and the outlet. Equipment are items such as a control valve, a heat exchanger, a filter, etc. It is likely that you will have to consult the manufacturer equipment literature to obtain this information.


Figure 1

The equation to calculate HX is:

eq. 1.1


You may find that the calculated pressure is negative, it is negative with respect to the outlet pressure. This can occur if the position of the point where you require the pressure is higher than the outlet and the friction between these two points is minimal.


The formula for converting pressure head to pressure is:

eq. 1.2


Determine the pressure anywhere on the suction side of the pump (see Figure 2 below)

Everything that was said above for calculating the pressure anywhere on the discharge side of the pump is true for calculating the pressure on the suction side of the pump. In this case, the conditions at the inlet of the system must be known and this is generally the conditions at the liquid surface of the suction tank.


z1: the elevation of the inlet point of the system with respect to the datum plane;


zx: the elevation of point X with respect to the datum plane where the pressure is required;


v1: velocity of the fluid at the inlet, the inlet is often the surface of a suction tank, this velocity is small and close to zero;


H1: the pressure head at the inlet of the system, if the tank is pressurized then H1 is the pressure head corresponding to the pressure in the tank;


SG: the specific gravity of the fluid (non-dimensional), water has an SG value of 1.0.


The pipe friction Hf or HF1-X in the equation 1.3 below, between the point where the pressure is required, point X, and the inlet must also be known. This is the friction loss in the pump suction line. You will have to calculate this using the Darcy and Colebrook equations or tables that are available in the Cameron Hydraulic data book, or tables in the Standards book from the Hydraulic Institute.


Lastly, you need to know the equipment friction loss HEQ or HEQ1-X in the equation 1.3 below, for all the equipment between the point where the pressure is required, point X, and the inlet. Equipment are items such as a control valve, a heat exchanger, a filter, etc. Equipment is rarely installed in the pump suction line so that this term is typically zero. It is likely that you will have to consult the manufacturer equipment literature to obtain this information.

Figure 2


The equation to calculate HX is:

Eq. 1.3

You may find that the calculated pressure is negative, it is negative with respect to the inlet pressure. This can occur if the position of the point where you require the pressure is higher than the inlet and the friction between these two points is minimal.