Enter the dynamic viscosity, length and diameter of the pipe, and the flow rate into the calculator to determine the flow resistance. This calculator helps in understanding the resistance to flow in a pipe due to viscosity.

Steady, incompressible Newtonian flow. Laminar equations require fully developed flow in a circular pipe; verify the regime before design use.

Presets and assumptions

Approximate references. Oil value is illustrative; grade alone does not set viscosity.

Actual bore, not nominal pipe size.

Related Calculators

Flow Resistance Formula

The following formula is used to calculate the pressure drop for fully developed laminar flow of a Newtonian fluid in a round pipe.

Δ P = (128 μ L Q) / (π d⁴)

Variables:

  • ΔP is the pressure drop (Pa); the pressure gradient is ΔP/L (Pa/m)
  • (mu) is the dynamic viscosity of the fluid (Pa·s)
  • L is the length of the pipe (m)
  • d is the diameter of the pipe (m)
  • Q is the flow rate (m³/s)

For laminar flow, pressure drop equals 128 times dynamic viscosity, pipe length and volumetric flow, divided by π times the fourth power of the internal diameter. Hydraulic resistance is ΔP/Q, in Pa·s/m³.

What is Flow Resistance?

Flow resistance is a measure of the opposition to fluid flow in a pipe, which is caused by the friction between the fluid and the pipe walls as well as the viscosity of the fluid. It is an important parameter in fluid dynamics and engineering, as it affects the pressure required to maintain a certain flow rate within a piping system.

How to Calculate Flow Resistance?

The following steps outline how to calculate the Flow Resistance.

  1. First, determine the dynamic viscosity of the fluid ((mu)) in Pa·s.
  2. Next, determine the length of the pipe (L) in meters.
  3. Next, determine the diameter of the pipe (d) in meters.
  4. Next, determine the flow rate (Q) in cubic meters per second.
  5. Next, gather the formula from above = ΔP = 128 μ L Q / (π d⁴).
  6. Finally, calculate pressure drop ΔP in pascals, or divide by pipe length for the pressure gradient in Pa/m.
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

dynamic viscosity ((mu)) = 0.001 Pa·s

length of the pipe (L) = 10 m

diameter of the pipe (d) = 0.05 m

flow rate (Q) = 0.00001 m³/s (chosen for a laminar-flow example; verify Reynolds number using the fluid density)