Calculating the internal diameter of a pipe based on the flow rate and fluid velocity is straightforward using a fundamental hydraulic principle.
You can calculate the internal pipe diameter by rearranging the basic flow equation that relates flow rate, velocity, and the pipe's cross-sectional area. As stated in the reference, the core relationship is Q = v · A, where:
- Q is the flow rate (volume per unit time)
- v is the velocity of the fluid
- A is the cross-sectional area of the pipe
Understanding the Relationship
The flow rate (Q) represents the volume of fluid passing a point in the pipe per second or minute. The velocity (v) is how fast the fluid is moving. The area (A) is the internal area of the pipe's opening, perpendicular to the flow direction. The formula simply means that the volume flow rate is the product of how fast the fluid is moving and the area it's flowing through.
Deriving the Diameter Formula
Since the pipe is typically circular, its cross-sectional area (A) is calculated using the formula for the area of a circle:
A = πr² or A = π(d/2)²
where:
- r is the internal radius of the pipe
- d is the internal diameter of the pipe
- π (pi) is approximately 3.14159
Now, substitute the area formula into the flow rate equation:
Q = v · (πd²/4)
To find the internal diameter (d), we need to rearrange this equation:
- Divide both sides by
v:
Q / v = πd² / 4 - Multiply both sides by
4:
(Q / v) · 4 = πd² - Divide both sides by
π:
(4Q) / (vπ) = d² - Take the square root of both sides to solve for
d:
d = √((4Q) / (πv))
This formula allows you to calculate the required internal pipe diameter if you know the desired flow rate (Q) and the acceptable fluid velocity (v).
Practical Application and Units
To use the formula effectively, ensure that your units are consistent. Here's a table of common units:
| Variable | Common Units (Metric) | Common Units (Imperial/US) |
|---|---|---|
| Q | m³/s, L/s, m³/h | ft³/s, gal/min (GPM) |
| v | m/s | ft/s |
| d | m | ft |
- Important: If your input units for Q and v are not compatible with the desired output unit for d (e.g., Q in L/s, v in m/s, want d in mm), you must convert them before using the formula. For example, if Q is in L/s, convert it to m³/s by dividing by 1000. If you calculate d in meters, multiply by 1000 to get millimeters.
Example Calculation
Let's say you need a flow rate (Q) of 0.01 m³/s and want to limit the velocity (v) to 2 m/s to minimize pressure drop.
Using the formula:
d = √((4 * 0.01 m³/s) / (π * 2 m/s))
d = √((0.04 m³/s) / (6.283 m/s))
d = √(0.006366 m²)
d ≈ 0.0798 m
To get the diameter in millimeters:
d ≈ 0.0798 m * 1000 mm/m ≈ 79.8 mm
So, you would need a pipe with an internal diameter of approximately 79.8 mm to achieve a flow rate of 0.01 m³/s at a velocity of 2 m/s. You would then typically select the nearest standard pipe size that meets or exceeds this calculated internal diameter.
This calculation is the core principle behind pipe diameter calculators, which simply automate this process.
