A cylindrical vessel open at the top is 20 cm high and 10 cm in diameter. A circular hole whose cross-sectional area 1 cm2 is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate 100 cm3 s–1. The height (in cm) of water in the vessel under steady state is (Take g = 1000 cm s

Engineering

Physics

BernoulIis Equation and Equation of Continuity

Question

A cylindrical vessel open at the top is 20 cm high and 10 cm in diameter. A circular hole whose cross-sectional area 1 cm² is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate 100 cm³ s^–1. The height (in cm) of water in the vessel under steady state is (Take g = 1000 cm s^–2)

20 cm

5 cm

10 cm

15 cm

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At steady state,
Rate of (inblow of water) = Rate of volume outflow of water
⇒ AV = 100 cm²s^–1
1 × v = 100
v = 100 cm/sec

⇒ v = $\sqrt{2 gh}$
$\Rightarrow 100 = \sqrt{2 \times 1000 \times h}$
⇒ h = 5 cm