For a two-dimensional in compressible flow field given

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For a two-dimensional in compressible flow field given by ū = A(x̂ i – yĵ), where A > 0, which one of the following statements is FALSE?
A. It satisfies continuity equation
B. It is unidirectional when x → 0 and y → ∞.
C. Its streamlines are given by x = y.
D. It is irrotational

1. A
2. B
3. C
4. D

Correct Option: C

C is the false statement
2D in compressible flow continuity equation.

	δu	+	δv	= 0
	δx		δy

	δ(Ax)	+	δ(- Ay)	= 0
	δx		δy

A – A = 0 it satisfies continuity equation.
⇒ As V̄ = Ax î - Ayĵ
As y → ∞ velocity vector field will not be defined along y axis.
So flow will be along x-axis i.e. 1-D flow.
⇒ Stream line equation for 2D

	dx	=	dy
	u		v

	dx	=	dy
	Ax		- Ay

In x = – ln y + ln c
ln xy = ln c
xy = c → streamline equation