The velocity profile in fully developed laminar flow in

The velocity profile in fully developed laminar flow in a pipe of diameter D is given by u = u₀ (1– 4r²/D²), where r is the radial distance from the center. If the viscosity of the fluid is ρ, the pressure drop across a length L of the pipe is

By Hagen – Poiseuille law, for steady laminar flow in circular pipes

τ = –μ	∂u
	∂r

τ =	–∂p	.	r
	∂x		2

μ	∂u	=	∂P	⋅	r
	∂r		∂x		2

μu₀		−8r		=	P	.	r
		D²			L		2

....		∵ u = u₀		1 −	4r²
					D²

=	–16μLu₀
	D²

[(–) sign is due to drop]