A fluid of dynamic viscosity 2 × 10

A fluid of dynamic viscosity 2 × 10^–5 kg/ms and density 1 kg/m³ flows with an average velocity of 1 m/s through a long duct of rectangular (25 mm × 15 mm) cross-section, Assuming laminar flow, the pressure drop (in Pa) in the fully developed region per meter length of the duct is _______.

Given, μ = 2 × 10^{– 5} kg/m.s, ρ = 1 kg/m³, u_av = 1m/sec
Duct area = 25 mm × 15 mm

∴	∆P	=	4 × λ × ρ × U²_av	..........(i)
	L		2 × Dⁿ

Here λ = Friction factor
D_n = Dia

∴ D_n =	4 × A	(A = Area, P = Parameter)
	P

λ =	4 × 25 × 15	= 18.75 mm .......(ii)
	2(25 + 15)

λ =	16	∴ Re =	ρ.u_av.D_n
	Re		π

∴ Re =	1 × 1 × 18.75 × 10^-3	= 937.5
	2 × 10^-5

∴ λ =	16	= 1.707 × 10^-2..........(iii)
	937.5

Here from equation (3),

∆P	=	4 × 1.707 × 10^-2 × (1)² × 2	= 1.82.8 Pa/m.
L		2 × 18.75 × 10^-3

V₁ = √2gH