Fluid Flow
CONTINUITY EQUATION
Volumetric Flow Rate
The volumetric flow rate ( ) of a system is a measure of the volume of fluid passing a point in
V
the system per unit time. The volumetric flow rate can be calculated as the product of the cross-
sectional area (A) for flow and the average flow velocity (v).
(3-1)
V
A v
If area is measured in square feet and velocity in feet per second, Equation 3-1 results in
volumetric flow rate measured in cubic feet per second. Other common units for volumetric flow
rate include gallons per minute, cubic centimeters per second, liters per minute, and gallons per
hour.
Example:
A pipe with an inner diameter of 4 inches contains water that flows at an average velocity
of 14 feet per second. Calculate the volumetric flow rate of water in the pipe.
Solution:
Use Equation 3-1 and substitute for the area.
V
(p r2) v
V
(3.14) (
2
12
ft)2 (14
ft
sec
)
V
1.22
ft3
sec
Mass Flow Rate
The mass flow rate
of a system is a measure of the mass of fluid passing a point in the
(
m)
system per unit time. The mass flow rate is related to the volumetric flow rate as shown in
Equation 3-2 where r is the density of the fluid.
(3-2)
m
r
V
If the volumetric flow rate is in cubic feet per second and the density is in pounds-mass per cubic
foot, Equation 3-2 results in mass flow rate measured in pounds-mass per second. Other
common units for measurement of mass flow rate include kilograms per second and pounds-mass
per hour.
Rev. 0
Page 9
HT-03
