The volume flow rate through a pipe is
- A(π·D4*∆p) / (128·μ·l)Correct
- B(π·D4 *∆p) / (64·μ·l)
- C(π·D2 *∆p) / (128·μ·l)
- DNone of the above
Solution
Concept
Hagen-Poiseuille Law
Formula
Q = (π × D4 × Δp) / (128 × μ × L)
Explanation
According to the Hagen-Poiseuille equation for steady laminar flow through a circular pipe, the volumetric flow rate (Q) in terms of radius (r) is Q = (π × r4 × Δp) / (8 × μ × L). Since the diameter (D) is equal to twice the radius (D = 2r or r = D/2), replacing r with D/2 gives Q = (π × D4 × Δp) / (128 × μ × L). Here, Δp is the pressure difference across the pipe length L, D is the pipe diameter, and μ is the dynamic viscosity of the fluid.
Correct answer: A) (π*D^4*∆p) / (128*μ*l)