# Poiseuilles Law Formula

TheÂ lawÂ ofÂ PoiseuilleÂ statesÂ thatÂ theÂ flowÂ ofÂ liquidÂ dependsÂ onÂ theÂ followingÂ variables such as the length of the tube(L), radius (r),Â pressure gradient (âˆ†P)Â and the viscosity of the fluid (Î·) in accordance with their relationship.

## The Poiseuilleâ€™s Law formula is given by:

Q = Î”PÏ€r4 / 8Î·l

Where in,

The Pressure Gradient (âˆ†P) ShowsÂ theÂ pressureÂ differentialÂ betweenÂ theÂ twoÂ endsÂ ofÂ theÂ tube,Â definedÂ byÂ theÂ factÂ thatÂ everyÂ fluidÂ willÂ alwaysÂ flowÂ fromÂ theÂ highÂ pressureÂ (P1)Â toÂ the low-pressure area (P2) and the flow rate is calculated by theÂ Â âˆ†P = P1-P2.

The radius of the narrow tube:

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

Viscosity (Î·):

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 / Ï€r4 and hence the Poiseuilleâ€™s law is

Q= (Î”P) 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 bloodâ€™s average speed.

Solution:

The blood viscosity Î· = 0.0027 N .s/m2

l = 20 cm

The difference of pressure = 380 Pa ( P1 â€“ P2)

The average speed is given byÂ

Q = Î”PÏ€r4 / 8Î·l

Q = (380Â Ã— 3.906Â Ã— 10-11Â Ã— 3.14)/(8Â Ã—Â 0.0027Â Ã— 0.20)

The average speed becomes 1.0789 m / s

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