There are two identical small holes of area of $$cross-section$$ a on the opposite sides of a tank containing a liquid of density ρ. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

Question

There are two identical small holes of area of $$cross-section$$ a on the opposite sides of a tank containing a liquid of density  ρ. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

Infinity Learn · Accepted Answer

Net force (reaction) $$=$$ $$F=FB$$−$$FA=dpBdt$$−dpAdt                                $$=avB$$ρ×vB−avAρ×vA∴  $$F=a$$ρ$$vB2$$−$$vA2$$                        …(i)According$$ to Bernoulli's theorem $$pA+12$$ρ$$vA2+$$ρ$$gh=pB+12$$ρ$$vB2+0$$⇒$$12$$ρ$$vB2$$−$$vA2=$$ρgh⇒$$vB2$$−$$vA2=2ghFrom$$ equation $$(i),  $$F=2a$$ρgh.

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