# Poiseuilles Law Formula

The law of Poiseuille states that the flow of liquid depends on the following variables such as the length of the tube(L), radius (r), pressure gradient (∆P) and the viscosity of the fluid (η) in accordance with their relationship.

## The Poiseuille’s Law formula is given by:

Q = ΔPπr4 / 8ηl

Where in,

The Pressure Gradient (∆P) Shows the pressure differential between the two ends of the tube, defined by the fact that every fluid will always flow from the high pressure (P1to the low-pressure area (P2) and the flow rate is calculated by the  ∆P = P1-P2.

The radius of the narrow tube:

The flow of liquid direct changes with the radius to the power four.

Viscosity (η):

The flow rate of the fluid is inversely proportional to the viscosity of the fluid.

Length of the arrow tube (L):

The flow rate of the fluid is inversely proportional to the length of the narrow tube.

Resistance(R):

The resistance is calculated by 8Ln / πr4 and hence the Poiseuille’s law is

Q= (ΔP) R

### Solved Example

Example 1:

The blood flow through a large artery of radius 2.5 mm is found to be 20 cm long. The pressure across the artery ends is 380 Pa, calculate the blood’s average speed.

Solution:

The blood viscosity η = 0.0027 N .s/m2

l = 20 cm

The difference of pressure = 380 Pa ( P1 – P2)

The average speed is given by

Q = ΔPπr4 / 8ηl

Q = (380 × 3.906 × 10-11 × 3.14)/(8 × 0.0027 × 0.20)

The average speed becomes 1.0789 m / s

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#### 1 Comment

1. Sujay Haldar

It is very helpful to me ,thanks.