The ratio Vm/u0 is

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Direction: Consider a steady incompressible flow through a channel as shown below:

The velocity profile is uniform with a value of u₀ at the inlet section A. The velocity profile at section B downstream is

The ratio V_m/u₀ is

1. 1
  1 − 2(δ/H)
2. 1
3. 1
  1 −(δ/H)
4. 1
  1 + (δ/H)

Correct Option: C

Applying continuity equation at sections A and B, mass flow rate at inlet section A = mass rate at section B.

	∴ u =	V_mY
		δ

u₀H = V_m(H − 2δ) + 2	V_m		Y²		^δ
	δ		2		₀

u₀H = V_m(H − 2δ) + 2	V_m	×	δ²
	δ		2

u₀H = V_m(H − 2δ) + V_mδ
u₀H = V_mH − 2V_mδ + V_mδ
u₀H = V_mH − V_mδ
u₀H = V_m(H − δ)

or	V_m	=	H	=	1
	u₀		H − δ		1 − (δ/H)