# Volume of Fluid Displaced for Pumps

on . Posted in Drilling Engineering

### Volume of Fluid Displaced for a Duplex Pump Formula

$$V_{fd} \;=\; n_c \; SL \; [\; ( 2 \; p_d^2 ) - r_d^2 \;] \; \eta_v \;/\; 42 \;\; 294$$
Symbol English Metric
$$V_{fd}$$ = volume of fluid displaced $$bbl\;/\;stroke$$ -
$$n_c$$ = number of cylinders $$dimensionless$$ -
$$SL$$ = stroke length $$in$$ -
$$p_d$$ = piston diameter $$in$$ -
$$r_d$$ = rod diameter $$in$$ -
$$\eta_v$$  (Greek symbol eta) = volumetric efficiency $$dimensionless$$ -

### Volume of Fluid Displaced for a Single-acting Pump Formula

$$V_{fd} \;=\; \pi \; p_d^2 \; SL \; n_c \;/\; 4$$
Symbol English Metric
$$V_{fd}$$ = volume of fluid displaced $$bbl$$ -
$$\pi$$ = Pi $$3.141 592 653 ...$$ -
$$p_d$$ = piston diameter $$in$$ -
$$SL$$ = stroke length $$in$$ -
$$n_c$$ = number of cylinders $$dimensionless$$ -

### Volume of Fluid Displaced for a Triplex Pump Formula

$$V_{fd} \;=\; SL \; p_d^2 \; \eta_v \;/\; 42 \;\; 98.03$$
Symbol English Metric
$$V_{fd}$$ = volume of fluid displaced $$bbl\;/\;stroke$$ -
$$SL$$ = stroke length $$in$$ -
$$p_d$$ = piston diameter $$in$$ -
$$\eta_v$$  (Greek symbol eta) = volumetric efficiency $$dimensionless$$ -