An ideal fluid of density 800 kgm ⁻³, flows smoothly through a bent… | JEE Main 2022 (26 Jun, Shift 1)

Q21JEE Main 2022 · 26 JUN · SHIFT 1Medium

Bernoulli's Equation

An ideal fluid of density 800 kgm ${}^{-3}$ , flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to $\frac{a}{2}$ . The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $\frac{\sqrt{x}}{6}$ ms ${}^{-1}$ for x = ___________. (Given g = 10 ms ${}^{-2}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 363

Continuity: area $a \to \frac{a}{2}$ , so $v_2 = 2v_1$ . The wide end is $h = 1$ m higher.
Bernoulli: $P_1 + \frac{1}{2}\rho v_1^2 + \rho g h = P_2 + \frac{1}{2}\rho v_2^2$
$(P_1 - P_2) + \rho g h = \frac{3}{2}\rho v_1^2 \Rightarrow 4100 + 800(10)(1) = \frac{3}{2}(800)v_1^2$
$12100 = 1200\,v_1^2 \Rightarrow v_1 = \frac{11}{\sqrt{12}} = \frac{11\sqrt{3}}{6} = \frac{\sqrt{363}}{6}\text{ m/s}$
So $x = 363$ .

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