Flow rate can be tricky to calculate, but if you have all of the required pieces we can create some easy Excel formulas to do the work for you.
Contents:
What is Flow Rate
Flow rate, often denoted as 'Q', is an essential metric in numerous engineering fields. It helps to quantify the volume of fluid passing per unit of time under certain conditions. Two of the most fundamental formulas for calculating flow rate are
Q = A * v (for open channels and ducts) and
Q = (πΔpr4) / (8μL)(for fluid flow in pipes under pressure).
When Should you Use Each Flow Rate Formula?
Q = A * v This formula is primarily used in hydrodynamics to determine the flow rate in open channels (like rivers or streams) and ducts, where the fluid is flowing freely and is not under any significant pressure. This formula requires you to know the cross-sectional area (A) and the velocity (v) of the fluid. It is based on the basic principle of conservation of mass and assumes a uniform, steady flow.
Q = (πΔpr4) / (8μL) This formula is derived from the Hagen-Poiseuille equation, which describes the flow of viscous fluids through a pipe. It's used when the fluid is under pressure, as in a closed pipe system. This formula requires knowledge of the fluid viscosity (μ), length of the pipe (L), pressure change (Δp), and pipe radius (r). This formula is most applicable for laminar flow conditions, long, narrow pipes, and incompressible, Newtonian fluids.
How to Calculate Flow Rate for an Ideal Fluid
Q = A * v is one of the simplest ways to calculate flow rate, where 'A' is the cross-sectional area of the flow and 'v' is the velocity of the flow. We are assuming the flow is uniform, meaning the velocity is constant across the cross-section.
Begin by inputting your data. In one column, list all your cross-sectional areas, and in another, list all your velocities.
If you know the area of the pipe, you do not need the diameter or the radius of the pipe. But if not, you'll need to calculate the cross-sectional area using the formula for the area of a circle (A = πr²).
So we take our diameter, and input this formula to convert to area. B3 being your diameter.
= PI()*(B3/2)^2= PI()*(diameter/2)^2
Next, input the corresponding velocity values for each cross-section.
Finally, write the formula to calculate the flow rate (Q = A * v) as = D3/144 * C3. We're dividing the velocity by 144 here to convert from square inches used in our area calculation to the square feet that velocity is in.
= D3/144*C3= velocity * area
Remember to double-check your units of measurement to ensure they're consistent across all your data and calculations. For instance, if your area is measured in square meters (m²) and your velocity is measured in meters per second (m/s), your flow rate will be in cubic meters per second (m³/s).
How to Calculate Flow Rate Using Pressure Change
If you need to calculate the flow rate of a fluid under pressure, a second formula is needed. The formula you'll need to use is called the Hagen–Poiseuille equation:
Q = (πΔpr4/8μL)Let's start by breaking down each term in the formula.
Q - The flow rate, which is the volume of fluid that flows past a given point per unit time
Ï€ - Mathematical constant pi, approximately equal to 3.14159
Δp - Pressure change across the length of the pipe
r - radius of the pipe
μ - Dynamic viscosity of the fluid. It's a measure of a fluid's resistance to shear or flow
L - Length of the pipe through which the fluid is flowing
Once you have all of the pieces of the formula down in a table like so:
We can calculate the flow rate with the following formula:
= (PI() * pressure_change * (radius^4))/(8 * viscosity * length)= (PI()*D10*(E10^4))/(8*B10*C10)
