An ideal liquid of density ρ is pushed with velocity v through the central limb of the tube shown in the figure. What force does the liquid exert on the tube ? The cross-sectional areas of the three limbs are equal to A each. Assume stream-line flow.

Engineering

Physics

Equation of Continuity

Question

$\frac{5}{4}$ ρAv²

$\frac{9}{8}$ ρAv²

ρAv²

$\frac{3}{2}$ ρAv²

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Velocity of liquid through inclined limbs = $\frac{v}{2}$
Rate of change of momentum of the liquid = ρAv² + 2 $[ρA {(\frac{v}{2})}^{2} \cos 60 °]$ = $\frac{5}{4} {ρAv}^{2}$

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