Water flows through a horizontal tube as shown in the figure. The… | JEE Main 2026 (21 Jan, Shift 1)

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Bernoulli's Equation

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at $A$ and $B$ are $6\text{ cm}^2$ and $3\text{ cm}^2$ respectively. The rate of flow will be $\underline{\hspace{3em}}\ \text{cm}^3/\text{s}$ . (take $g = 10\text{ m/s}^2$ )

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Answer: (d)

Pressure difference from the columns: $P_A - P_B = \rho g h$ .
Bernoulli: $\frac{1}{2}(v_B^2 - v_A^2) = gh = 10\times0.05 = 0.5 \Rightarrow v_B^2 - v_A^2 = 1$
Continuity: $v_B = \dfrac{6}{3}v_A = 2v_A \Rightarrow 3v_A^2 = 1 \Rightarrow v_A = \dfrac{1}{\sqrt{3}}\text{ m/s} = \dfrac{100}{\sqrt{3}}\text{ cm/s}$
$Q = A_A v_A = 6\times\dfrac{100}{\sqrt{3}} = 200\sqrt{3}\text{ cm}^3/\text{s}$
So the answer is (d).

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