# Poiseuille's Law

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Equation / Last modified by KurtHeckman on 2018/07/27 17:07
Q =
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JustinLiller.Poiseuille's Law
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The Poiseuille's Law calculator computes the flow rate in a pipe based on the change of pressure, the length of pipe, the inner radius and the viscosity of fluid.

INSTRUCTIONS: Choose units and enter the following:

• (P1) This is the initial pressure • (P2) This is the final pressure
• (r) This is the inner radius of the pipe
• (L) This is the length of the pipe
• (η) This is the viscosity of the fluid

Poiseuille's Law Flow Rate (Q): The calculator returns the flow rate in milliliters per minute (mL/min).  However, the can be automatically converted to compatible units via the pull-down menu.

#### The Math / Science

The relationship between pressure and continuous laminar flow of fluid in a rigid tube is described by Poiseuille's law, which states that the flow rate of a fluid, Q, is directly proportional to the pressure difference, along the length of the tube and the fourth power of the radius of the tube, and inversely proportional to the tube length, and fluid viscosity.  The formula for Poiseuille's Law is:

Q = ((P_1 - P_2) πr^4)/(8Lη)

where:

• Q is the volume flow rate
• P1 is the initial pressure
• P2 is the final pressure
• r is the inner radius
• L is the length
• η is the viscosity of fluid