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Poiseuille Equation – Chemistry Optional Notes – For W.B.C.S. Examination.
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.Continue Reading Poiseuille Equation – Chemistry Optional Notes – For W.B.C.S. Examination.
It is given by:
the flow rate ( or )
the radius of the tube (cm or m)
the outlet fluid pressure ( or )
the inlet fluid pressure ( or )
the dynamic viscosity of the fluid (poise or Pa.s)
the length of the tube (cm or m)
The entire relation or the Poiseuille’s Law formula is given by
Q = ΔPπr4 / 8ηl
Wherein,
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 (P1) to 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
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
Radius = 2.5 mm
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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