Poiseuille's Law Calculator

The detailed process to obtain the flow rate and flow resistance of the fluids easily with the Poiseuille flow equation is mentioned below. Follow these steps and check the answer.

• Multiply the change in pressure with π.
• Multiply the product with radius to the power 4.
• Divide the result by 8 times of product of dynamic viscosity and pipe length to check flow rate value.
• Multiply the 8 times of pipe length with dynamic viscosity.
• Divide the result by product of pie and radius to power 4 to get the flow resistance.

Poiseuille's equation is also called Hagen-Poiseuille's equation which is the formula used in fluid dynamics. It describes the laminar flow of fluids in a cylindrical container (pipe).

Hagen-Poiseuille's equation tells the amount of water that flows through the pipe in one second by using the fluid viscosity, pipe length, pipe radius and difference in pressure. It will find the volumetric flow rate and resistance of the fluids easily.

The formulas to calculate the flow rate and flow resistance are given below:

Q = (π * Δp * r4)/(8 * μ * l)

R = (8 * μ * l)/(π * r4)

Where,

Q is the volumetric flow rate

R is the resistance

μ is the dynamic viscosity

l is the pipe length

r is the radius of the pipe

Δp is change in pressure

Example

Question: An intravenous (IV) system is supplying saline solution to a ratient through a needle of radius of 0.15 mm and length 2.50 cm. The change in pressure of the needle is 8.00 mm Hg and assuming the viscosity of the saline solution to be the same as that of water. Find the volumetric flow and resistance?(Assume that the temperature is 20°C)

Solution:

Given that

Radius of the needle r = 0.15 mm = 0.15 x 10-3 m

Length of the needle l = 2.50 cm = 2.50 x 10-2 m

Change in pressure Δp = 8 mm Hg = 1.066 x 103 N/m2

Viscosity μ = 1 x 10-3 N.s/m²

Volumetric flow rate formula is Q = (π * Δp * r4)/(8 * μ * l)

Q = (π * 1.066 x 103 * (0.15 x 10-3)4)/(8 * 1 x 10-3 * 2.50 x 10-2)

(3.14 * 1.066 x 103 * 5.062 x 10-16)/(20 x 10-5)

= 0.8471 x 10-8

R = (8 * μ * l)/(π * r4)

R = (8 * 1 x 10-3 * 2.50 x 10-2)/(π * (0.15 x 10-3)4)

= (20 x 10-5)/(1.589 x 10-15)

= 12.58 x 1010

Therefore, volumetric flow is 0.8471 x 10-8 and flow resistance is 12.58 x 1010

Clarify your queries right after class and seek help on all physics concepts all at one place on Physicscalc.Com

1. What are the assumptions used for the Poiseuille formula?

The assumptions of the Poiseuille equation are that the fluid is incompressible and Newtonian. The flow is laminar through a cylindrical tube of the constant circular cross-section that is substantially longer than its diameter.

2. What is the laminar flow?

In fluid dynamics, laminar flow is defined by the fluid particles following smooth paths in layers with each layer moving smoothly.

3. What is Poiseuille's equation?

The flow of fluids through a cylindrical pipe can be described by Poiseuille's Law. The law states that the flow of fluids is related to different factors such as fluid viscosity, pressure gradient, pipe length and diameter.

4. What is the Poiseuille flow equations for resistance and flow rate?

Poiseuille flow equation for volumetric flow rate is Q = (π * Δp * r4)/(8 * μ * l) and for flow resistance is R = (8 * μ * l)/(π * r4)