Pressure difference at pipe ends from dynamic viscosity and flow rate

In non-ideal fluid mechanics, the Hagen—Poiseuille equation is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw.

Conditions:

1. The fluid is incompressible and Newtonian.

2. The flow of the fluid is laminar.

3. The pipe is long enough for the flow to be laminar.

4. The pipe has constant cross section.

Links:

1. Wikipedia, first part of the first equation.

dynamic_viscosity

dynamic_viscosity of the fluid.

Symbol:

mu

Latex:

\(\mu\)

Dimension:

pressure*time

length

length of the pipe.

Symbol:

l

Latex:

\(l\)

Dimension:

length

flow_rate

volumetric_flow_rate of the fluid through the pipe.

Symbol:

Q

Latex:

\(Q\)

Dimension:

volume/time

radius

radius of the pipe.

Symbol:

r

Latex:

\(r\)

Dimension:

length

pressure_difference

Difference in pressure between the two ends of the pipe.

Symbol:

Delta(p)

Latex:

\(\Delta p\)

Dimension:

pressure

law

Delta(p) = 8 * mu * l * Q / (pi * r^4)

Latex:

\[\Delta p = \frac{8 \mu l Q}{\pi r^{4}}\]