Nuclei Class 12th Physics Physics Nuclei

**A liquid of density 750 kgm^-3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A₁ = 1.2 * 10^-2m² 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_________ * 10^-3m³s^-1.**

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Alok Kumar Singh | Contributor-Level 10

8 months ago

Given A₂ = $\frac{_{}}{}$ $\frac{A_{1}}{2}$

Bernoulli's b/w (1) & (2)

$\frac{P_{1}}{ρ g} + \frac{v_{1}^{2}}{2 g} + z_{1} = \frac{ρ_{2}}{ρ g} + \frac{v_{2}^{2}}{2 g} + z_{2}$

[z₁= z₂]

$\frac{P_{1} - P_{2}}{ρ g} = \frac{v_{2}^{2} - v_{1}^{2}}{2 g}$

[Q = A₁V₁ = A₂V₂]

$\frac{4500}{750} = \frac{{(\frac{Q}{A_{2}})}^{2}}{2} - {(\frac{Q}{A_{1}})}^{2}$

$12 = Q^{2} [\frac{1}{A_{2}^{2}} - \frac{1}{A_{1}^{2}}]$

$Q = 2 A_{1} = 2 * 1.2 * 1 0^{- 2}$

= 2.4 * 10^-2 m³ /sec

= 24 * 10^-3 m³ /sec

= 24

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