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 off the three l

Question

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 off the three limbs are equal to A each. Assume stream-line flow.

TestHub · Accepted Answer

Continuity at the symmetric outlets: A v = 2 A u ⇒ u = 2 v ​ The two outlet momentum-flux components along the inlet axis are: 2 ( ρ A u 2 cos 6 0 ∘ ) = 2 [ ρ A ( 2 v ​ ) 2 2 1 ​ ] = 4 1 ​ ρ A v 2 The inlet momentum flux is: ρ A v 2 The force magnitude on the tube is: F = ρ A v 2 + 4 1 ​ ρ A v 2 = 4 5 ​ ρ A v 2 Hence B.

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