The Hagen-Poiseuille equation is a fundamental formula that describes the flow of a viscous fluid through a cylindrical pipe or tube. It was formulated by Gotthilf Hagen and Jean Léonard Marie Poiseuille in the 19th century, and it remains a cornerstone of fluid dynamics.
Theoretically and practically it has been proved that when a fluid flows viscously in a pipe of cross-section then according to the Hagen Poiseuille equation.Â
Hagen Poiseuille equation is much more useful for determining when the other terms are known.
ΔP = 32Lvμ/gcD²
Where,Â
ΔP = Pressure drop Lb/sq ft.
L = Length of tubeÂ
μ = Viscosity (Lb - mass/ft sec)
gc = 32.2 (Lb - mass)F/(Lb - force)sec²Â
v = Velocity
D = Diameter of the tubeÂ
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Friction Loss in Pipe
When there is liquid flow in a pipe, friction resistance arises due to the roughness of the surface of the pipe. As a result, some energy of the liquid will be lost, which is called friction head loss in pipes. It is represented by hf.
Friction loss in pipe formulaÂ
hf = 4flv²/2gd Â
WhereÂ
hf = Friction head loss in pipeÂ
f = Friction factor or coefficient of friction
l = Length of pipe
d = Diameter of pipe
v = Velocity of fluidsÂ
Effect of Roughness in pipe and tubeÂ
Generally, every pipe and tube is rough. Pipes are made very rough as compared to tubes. Due to this roughness of the pipe, the head loss of the pipe is more than that of the smooth pipe.Â
The height of roughness is represented by K, it is called the roughness parameter. Friction factor, Reynolds Number, and Relative roughness are formed on the basis of dimensional analysis.Â
Relative Roughness = K/DÂ
Where
K = Height of single unit of roughness
D = Diameter of pipeÂ
Note:- (1) If the clear pipe is smoothened then the value of the friction factor decreases.Â
(2) If the friction factor does not decrease on re-smoothing the pipe for a fixed Rn, it is said to be hydraulically smooth.
The Hagen-Poiseuille Equation Applications
The Hagen-Poiseuille equation finds numerous practical applications in various industries.
1. Plumbing and Water Systems
Engineers use this equation to design efficient water supply systems, ensuring smooth water flow through pipes of different diameters.
2. Medical Applications
Understanding blood flow in vessels is essential for medical professionals. The Hagen-Poiseuille equation helps in evaluating blood flow rate and identifying potential issues.
3. Industrial Processes
In industrial settings, this equation aids in optimizing fluid flow through pipelines, ensuring the smooth transportation of chemicals and other materials.
4. Engineering Design
Engineers rely on the equation to design pipelines, optimize heat exchangers, and create systems that involve fluid transportation.
