Two streams of water flow through the U - shaped tubes shown. The tube on the left has cross-sectional area 2A, and the speed of the water flowing through it is v; the tube on the right has cross - sectional area A0 = A. If the net force on the tube assembly is zero, what must be the speed v0 of the water flowing through the tube on the right? Neglect gravity, and assume that the speed of the water in each tube is the same upon entry and exit.

Engineering

Physics

Momentum and Energy Conservation for System of Particles

BernoulIis Equation and Equation of Continuity

Question

Two streams of water flow through the U - shaped tubes shown. The tube on the left has cross-sectional area 2A, and the speed of the water flowing through it is v; the tube on the right has cross - sectional area A₀ = A. If the net force on the tube assembly is zero, what must be the speed v₀ of the water flowing through the tube on the right?

Neglect gravity, and assume that the speed of the water in each tube is the same upon entry and exit.

$\frac{v}{\sqrt{2}}$

$\sqrt{2} v$

$\frac{1}{2} v$

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$F = 2 ρ \times 2 {Av}^{2} = 2 ρ \times A \times v_{0}^{2}$

$y_{0} = \sqrt{2} v$ .