The relationship of Volumetric Flow Rate to Velocity should be calculated properly for the pipeline design of an industry.
Volumetric Flow Rate is the volume of a fluid flows through a tube, duct, channel or other this type of structure per unit time. Velocity refers how fast a fluid is moving through a particular passage per unit time.
Volume Flow Rate, Q or V=Av
Where A= Cross sectional area of a section in m2
And v=Average velocity of the fluid through out the section in m/s
The unit of Volume Flow Rate is m3/s(cubic meters/second), m3/h(cubic meter/hour), l/s (litre/second), l/min.(litre/minute),ml/s(millilitre/second) etc.
Suitable unit is decided as per the magnitude of Volumetric Flow Rate. In case of very small flow rate(for example fluid inside a syringe), ml/s is preferred and for very large volume flow rate(for example flow of water in a river), it is expressed in m3/h.
Flow Velocity, v =s/t
Velocity is denoted by small v
Where s= Distance covered by the fluid molecules
And t=Time period
The unit of Velocity is m/s (meter/second), km/h(kilometre/hour) etc.
Is Volume Flow Rate the same as Velocity?
Volume Flow Rate and Velocity are related to each other but if we consider as physical quantities, both of them are quite different from each other.
In simple words Velocity of a fluid refers to how fast the fluid (gas or liquid)moves through a passage in a particular time period. Volume Flow Rate gives us the quantity or volume of a fluid (gas or liquid) flows through a passage within a time period.
Velocity of a fluid is a vector quantity whereas Volume Flow Rate is a scalar quantity since it is a time derivative of volume.
Difference between Volumetric Flow Rate To Velocity
The difference between Volumetric Flow Rate and Velocity as follows:
| Volumetric Flow Rate | Velocity |
| Volume Flow Rate(Q) is the amount of volume(V) of a fluid flows through a cross sectional area (A) per unit time (t). | Velocity of a fluid is defined as the distance(d) travelled by a fluid within a time period( t). |
| Mathematically, Q = V/t | Mathematically, |
| Units: m3/s( SI unit), cm3/s (CGS unit) | Units: m/s(SI unit), cm/s(CGS unit) |
Relationship of Volumetric Flow Rate To Velocity
If we observe the flow rate of a stream or river, if the velocity of water is high, the Volume Flow Rate of the river is also high.
The following equation gives us the relationship between Volume Flow Rate(Q) and Velocity(v).
Q=A. v
Here A is the cross sectional area and v is the velocity of the fluid.
Generally we consider here the average velocity since the velocity of flow does not remain constant throughout the particular time period. Hence,
Eq(1)
From Eq (1), it is clear that Volume Flow Rate is directly proportional to both average velocity of the flow and the size of the passage( may be pipe, duct or a river).
The larger the diameter of the pipe or duct, greater is the cross sectional area
In the above figure we can see a pipe with cross sectional area A in m2 and velocity or speed of the fluid is (small v bar)in m/s.
To find out the flow rate or discharge in a process application, two measurements are required: the volume of fluid that crosses the passage and time required by this volume to cross the passage.
Volume Flow Rate,Q= Volume/time
Volume(Capital V) in cubic meter m3 and time(t) in second.
Q=V/t Eq(2)
In the above figure the volume(V) of fluid that passes through the point(O) within a time period t is represented by the shaded portion of the cinduit is given by
Volume,V=A.d
From Eq(2) Q= V/t = A.d/t
Q = A.d/t Eq(3)
Now average velocity,
Thus the Eq(3) becomes
Volume Flow Rate,
In case of an incompressible fluid(like water) flows through a passage with different cross sectional area, the Volumetric Flow Rate of the fluid remains constant. To maintain the constant flow rate, the speed of flow is low at a larger cross sectional area of the pipe and speed becomes high at a smaller cross sectional area.
In the above figure we can see an incompressible liquid flows through a pipe of decreasing cross sectional area. Since the fluid is incompressible in nature it tries to maintain continuity and same volume of fluid flows through each point of the pipe irrespective of the size or diameter of the pipe.
When the size of the pipe is wider at point 1, the velocity of the flow will decrease in comparison to the velocity at point 2 where the pipe becomes narrow. In this way the Flow Rate at each point of the pipe is maintained at a constant value.
At point 1 and 2,
Q1 = Q2
Or,
This is the famous Continuity Equation applicable for Incompressible fluids.
How to find Velocity from Volumetric Flow Rate?
In case of columns of different sizes, it is more convenient to represent flow of a fluid in terms of flow velocity (cm/h). But generally flow is calculated in terms of volume flow rate(ml/min).
Using the following formula we can easily calculate the Velocity of a flow from Volume Flow Rate of a fluid:
Flow Rate,
Where Q= Volume Flow Rate in m3/s
A =Cross sectional area of the passage through which fluid is flowing in m2
Now, bar v=Q/A=Volume Flow Rate/Cross sectional area of the pipe
Flow Rate can also be defined as the ration between the change in volume of the fluid and change in time.
Q=dV/dt
I am Sangeeta Das. I have completed my Masters in Mechanical Engineering with specialization in I.C Engine and Automobiles. I have around ten years of experience encompassing industry and academia. My area of interest includes I.C. Engines, Aerodynamics and Fluid Mechanics. You can reach me at