7. Water runs into a fountain, filling all the pipes, at a steady rate of 0.750 m³/s. (a) How fast will it shoot out of a hole 4.50 cm in diameter? (b) At what speed will it shoot out if the
diameter of the hole is three times as large?
V˙=vS=πvd24, ⟹ \dot V=vS=\frac{\pi vd^2}4,\impliesV˙=vS=4πvd2,⟹
v=4V˙πd2=472 ms,v=\frac{4\dot V}{\pi d^2}=472~\frac ms,v=πd24V˙=472 sm,
v1=v9=52 ms.v_1=\frac v9=52~\frac ms.v1=9v=52 sm.
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