A fan in the duct shown below sucks air from the ambient

A fan in the duct shown below sucks air from the ambient and expels it as a jet at 1 m/s to the ambient. Determine the gauge pressure at the point marked as A. Take the density of air as 1 kg/m³.

Applying Bernoulli’s equation between sections (i) & A

P₁ =		P_A	+	V_A²
		ρg		2g

		P_A - P₁	=	-V_A²
		ρg		2g

P₁ = Pambient
∴ P_A - P₁ = (P_A)gauge

∴		(P_A)gauge	==	-V_A²
		ρg		2g

(P_A)gauge =	-1 × 1²	= 0.5N/m²
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