At two points 1 and 2 in a pipeline, the velocities are

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At two points 1 and 2 in a pipeline, the velocities are V and 2V, respectively. Both the points are at the same elevation. The fluid density is ρ. The flow can be assumed to be in compressible, inviscid, steady and irrotational. The difference in pressures P₁ and P₂ at points 1 and 2 is

1. 0.5 ρV²
2. 1.5 ρV²
3. 2 ρV²
4. 3 ρV²

Correct Option: B

Bernoullis equation,

	P₁	+	V²	=	P₂	+	(2V)²	=	P₂	+	4V²
	ρg		2g		ρg		2g		ρg		ρg

	P₁ - P₂	=	3V²
	ρg	=	2g

∴ P₁ - P₂ = P × 1.5 V² = 1.5 ρV².