Answer to Article #57 quiz: "Pump NPSH and Developed Head"
The available NPSHA is a net (total) positive suction head, over vapor pressure of a pumped liquid. (A more detailed background on this can be found in a topic "How does pump suction limit the flow?").
We will first determine a total suction head (Hs), which is equal to static water level above the pump centerline plus the pressure (in units of head) at the liquid surface, minus the losses at the suction side of a pump.
80o water has specific gravity of 1.0, and atmospheric pressure, converted to feet of head is equal to 14.7 psia x 2.31 / 1.0 = 34.0 feet.
Then, Hs = 30+34-10 = 54 feet - a total suction head, in front of a pump.
Vapor pressure of 80 0F water is 0.5 psia, or 0.5 x 2.31 / 1.0 = 1.2 feet.
NPSHA can now be calculated as:
NPSHA = Hs - Hvapor = 54 - 1.2 = 52.8 feet.
Suction gage shows static pressure, which can be found by subtracting velocity head and a gage elevation (the higher the gage is positioned, the low its static pressure reading would be).
Velocity is equal to flow divided by the pipe net open area (with coefficient 0.321, if flow is in gpm, and area in square inches). Making a simplifying assumption that the net pipe open area is based on its nominal diameter, we get:
ASUCTION = 3.14 x 32 / 4 = 7.1 in2, and
VSUCTION = 200 x 0.321 / 7.1 = 9.1 ft/sec, and
Velocity head (dynamic) is hvel.suction = 9.12 / 64.4 = 1.3 feet
This now allows us to calculate the gage pressure in absolute units:
H_suction_gage (abs) = 54 - 1.4 - 4 = 48.6 feet, or, subtracting the atmospheric component:
H_suction_gage (gage) = 48.6 - 34 = 14.6 feet, which would translate into a psi(gage) units as:
P_suction_gage = 14.6 x 1.0 / 2.31 = 6.3 psig - this is what we would see on the gage dial.
Next, let's find a discharge head, which is (similar to suction) a sum of static pressure, velocity head, and correction for the gage elevation.
Discharge gage reads 100 psig, which is equivalent to 100+14.7 = 114.7 psig, and, in units of feet is: 114.7 x 2.31 / 1.0 = 265.0 feet.
Static pressure at the pump centerline is then: 265 + 20 = 285 feet.
Discharge pipe flow area is 3.14 x 22 / 4 = 3.1 in2, and
Vdisch = 200 x 0.321 / 3.1 = 20.4 ft/sec, producing a velocity head of
hvel suction = 20.42 / 64.4 = 6.5 feet.
Total discharge head is then Hd = 285 + 6.5 = 291.5 feet.
Pump developed head is a difference between the discharge and suction heads:
H=Hd - Hs
H = 291.5 - 54 = 237.5 feet, which is the equivalent to saying that the pump generates 237.5 x 1.0 / 2.31 = 102.8 psi differential pressure.
Note that simply taking a difference between a discharge a suction gage readings would give us 100 - 6.3 = 93.7 psi, i.e. almost a 9% error.
Usually the elevation between the gages is not as significant as is this example, and the flow velocities are usually lower (larger pipe), but, in general, it is important to remember to account for all components of the pump head, in calculations.