In a Laminar Flow through circular pipe, the Discharge (Q) varies :Group of answer choicesInversely with Pressure DropLinearly with Fluid ViscosityWith the square of Pipe RadiusInversely with Fluid Viscosity
Question
In a Laminar Flow through circular pipe, the Discharge (Q) varies :Group of answer choicesInversely with Pressure DropLinearly with Fluid ViscosityWith the square of Pipe RadiusInversely with Fluid Viscosity
Solution
In a laminar flow through a circular pipe, the discharge (Q) varies with the square of the pipe radius. This is based on the Hagen-Poiseuille equation for laminar flow, which states that Q = (πPd^4) / (128μL), where P is the pressure difference, d is the diameter of the pipe, μ is the dynamic viscosity of the fluid, and L is the length of the pipe. From this equation, we can see that the discharge (Q) is directly proportional to the fourth power of the radius (since radius is half of diameter, d=2r, and hence d^4 is proportional to r^4), and inversely proportional to the viscosity of the fluid. Therefore, the discharge does not vary linearly with fluid viscosity, nor does it vary inversely with pressure drop.
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