A liquid of density 750 kgm ⁻³ flows smoothly through a horizontal pipe that tapers in cross- sectional area from A1 = 1.2 × 10 - 2 m2 to A2 = A₁/2. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ___________ × 10 - 3 m3s ⁻¹. Numerical answer type. Work it out, then open the answer.

Answer: 24. Continuity: A₂ = A₁/2 ⇒ v₂ = 2v₁ Bernoulli: Δ P = 1/2ρ(v₂² - v₁²) = 3/2ρ v₁² 4500 = 3/2(750)v₁² = 1125 v₁² ⇒ v₁ = 2 m/s Q = A₁v₁ = (1.2×10⁻²)(2) = 24×10⁻³ m³/s So the answer is 24.

A liquid of density 750 kgm ⁻³ flows smoothly through a horizontal… | JEE Main 2022 (28 Jun, Shift 2)

Q20JEE Main 2022 · 28 JUN · SHIFT 2Medium

Bernoulli's Equation

A liquid of density 750 kgm ${}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross- sectional area from A1 = 1.2 $\times$ 10 $-$ 2 m2 to A2 = $\frac{A_1}{2}$ . The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ___________ $\times$ 10 $-$ 3 m3s ${}^{-1}$ .

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

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Answer: 24

Continuity: $A_2 = \frac{A_1}{2} \Rightarrow v_2 = 2v_1$
Bernoulli: $\Delta P = \frac{1}{2}\rho(v_2^2 - v_1^2) = \frac{3}{2}\rho v_1^2$
$4500 = \frac{3}{2}(750)v_1^2 = 1125\,v_1^2 \Rightarrow v_1 = 2\text{ m/s}$
$Q = A_1v_1 = (1.2\times10^{-2})(2) = 24\times10^{-3}\text{ m}^3\text{/s}$
So the answer is $24$ .

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