A frictionless fluid of density r flow through a bent pipe

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A frictionless fluid of density r flow through a bent pipe as shown below. If A is the cross sectional area and V is the velocity of flow, the forces exerted on segment 1-2 of the pipe in the x and y directions are, respectively.

1. ρAV² ; 0
2. ρAV² ; √2 ρAV²
3. 0 ; 0
4. 0 ; 1 ρAV²
  √2

Correct Option: C

Apply momentum equation between 2 sections
In x direction,
∑Fx = m( V_2x - V_1x )
= m (v – v) = 0
In Y direction,
∑Fx = m( V_2y - V_1y )
= m (0 – 0) = 0

0 ;	1	ρAV²
	√2