## II. FUNDAMENTALS OF OPERATION

### C. Calculations of Volumetric Efficiency

Volumetric Efficiency (EV) is defined as the ratio of actual pump capacity to ideal pump displacement. The EV calculation depends upon the internal configuration of each individual liquid end cylinder, plunger/piston size, and the liquid being pumped. Given full details regarding differential pressure, pumped liquid mixture, and expected temperature rise on the discharge stroke - WGI can calculate this efficiency.

**1. Calculating E _{V} for Water**

See TABLE 4 Page A31 for the water compressibility chart. An example of volumetric efficiency calculation for water is also shown.

**2. Calculating E _{V} for Hydrocarbons**

See TABLE 6 Page A34 for the physical properties of hydrocarbons. For compressible liquids such as these, horsepower calculations are slightly more complex than for incompressible liquids. However, the magnitude of the horsepower required will be slightly less than if calculated for the full displacement.

**3. Displacement Table**

Table 1 can be used to determine pump displacement and whether or not the proper efficiency is being obtained.

**Example 1:**

Find the capacity (Q), in Barrels Per Hour (BPH), for a single acting 3-1/2" x 4" triplex plunger pump operating at 95% volumetric efficiency (E_{V} ) and a speed of 350 rpm.

From TABLE 1 a 3-1/2" plunger with a 4" stroke will displace 0.167 gallons per stroke. This type of pump will displace liquid at a rate of 3 forward strokes only per revolution. Therefore, the displacement per revolution is 0.167 gal./stroke x 3 strokes/rev. = 0.501 gal./rev. (gpr). At 350 rpm, the total displacement is 175.35 gallons per minute (GPM). Dividing by 0.7 gives 250.5 BPH displacement (D). Therefore, the pump capacity at a 95% volumetric efficiency is Q = D Ev = 250.5 (95) (100) (100) Q = 237.9 BPH

**Example 2:** Find the rpm (n) required for a single acting 3" x 5" triplex plunger pump operating at EV = 85% and capacity (Q) = 200 BPH. D = displacement = Q (100) Ev D = 200 = 235.29 BPH 0.85 gpr = (0.153 gal./stroke) (3 strokes/rev.) gpr = 0.459 GPM = BPH x 0.7 = 235.29 x 0.7 GPM = 164.7 At the given displacement and volumetric efficiency, the pump speed (n) is n = GPM = 164.7 rpm gpr 0.459 n = 358.8 rpm

**Example 3: **Find the displacement (D), in gallons per minute (GPM), for a double acting 4" x 10" duplex piston pump running at a crankshaft speed of 60 rpm. Pump has 1-1/2" diameter piston rods. This type pump will displace liquid at a rate of; 2 forward strokes/rev. and 2 rearward strokes/rev. (the 2 rearward strokes/rev. will displace less liquid than 2 forward strokes due to the amount of volume taken up by the piston rod). Assume the pump EV = 95%. gpr = gprf + gprr Where, gprf = gal./rev. for the 2 forward strokes gprf = 0.544 x 2 = 1.088 gprr = gal./rev. for the 2 rearward strokes gprr = [0.544 - (0.544 - 0.077){piston rod}] x 2 gprr = 0.934 gpr = (1.088 + 0.934) = 2.022 gpr D = Q (100) = 2.022 (60)(95) = 115.3 GPM Ev 100

**Note 1:** One barrel equals 42 U.S. gallons. Gallons per minute (GPM) divided by 0.7 equals barrels per hour (BPH). Displacement is the ideal volume swept by the plunger or piston on the discharge stroke during any selected time period.

**Note 2:** Under the conditions and definitions given above, the pump must run at a higher rpm in order to displace enough volume to deliver the required amount of liquid.