In case of a pressure driven laminar flow of a Newtonian fluid of viscosity (μ) through a
horizontal circular pipe, the velocity of the fluid is proportional to
a)
μ
b)
μ^0.5
c)
μ-1
d)
μ^-0.5
Correct answer is option 'C'. Can you explain this answer?

Question

In case of a pressure driven laminar flow of a Newtonian fluid of viscosity (μ) through a
horizontal circular pipe, the velocity of the fluid is proportional to

a)
μ
b)
μ^0.5
c)
μ-1
d)
μ^-0.5

Correct answer is option 'C'. Can you explain this answer?

Answer

Μ) through a circular pipe of radius (R) and length (L), the Hagen-Poiseuille equation can be used to determine the flow rate (Q):

Q = πR^4ΔP / 8μL

where ΔP is the pressure difference between the ends of the pipe.

This equation assumes that the fluid is incompressible, the flow is laminar, and the pipe is straight and of constant cross-sectional area. It also assumes that there are no sources or sinks of fluid along the length of the pipe, and that the velocity profile across the pipe is parabolic.

The Hagen-Poiseuille equation can be used to determine the flow rate in a variety of applications, such as in the design of pipelines, heat exchangers, and microfluidic devices. It is important to note that this equation only applies to laminar flow, and that turbulent flow cannot be accurately described using this equation.

Answer

(a)

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