Water is flowing through a horizontal tube ac | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

According to Bernoulli's thereom

$\mathrm{P}_{1}+\frac{1}{2} \rho \mathrm{v}_{1}^{2}=\mathrm{P}_{2}+\frac{1}{2} \rho \mathrm{v}_{2}^{2}$

$\R

Vedclass · Accepted Answer

$32$

Vedclass · Answer

According to Bernoulli's thereom

$\mathrm{P}_{1}+\frac{1}{2} ho \mathrm{v}_{1}^{2}=\mathrm{P}_{2}+\frac{1}{2} ho \mathrm{v}_{2}^{2}$

$\Rightarrow P_{1}-P_{2}=\frac{1}{2} ho\left[v_{2}^{2}-v_{1}^{2}ight]$

Let rate of flow $Q=A_{1} v_{1}=A_{2} v_{2}$

$\mathrm{h} ho \mathrm{g}=\frac{1}{2} ho\left[\frac{\mathrm{Q}^{2}}{\mathrm{A}_{2}^{2}}-\frac{\mathrm{Q}^{2}}{\mathrm{A}_{1}^{2}}ight]$

$\Rightarrow 2 g h=Q^{2}\left[\frac{A_{1}^{2}-A_{2}^{2}}{A_{1}^{2} A_{2}^{2}}ight]$

$\Rightarrow Q=\sqrt{\frac{2 g h A_{1}^{2} A_{2}^{2}}{A_{1}^{2}-A_{2}^{2}}}$

$Q=A_{1} A_{2} \sqrt{\frac{2 g h}{A_{1}^{2}-A_{2}^{2}}}$

$=\pi r_{1}^{2} 	imes \pi r_{2}^{2} \sqrt{\frac{2 	imes 10 	imes 0.8}{\left(\pi r_{1}^{2}ight)^{2}-\left(\pi r_{2}^{2}ight)^{2}}}$

$=\frac{\pi^{2} r_{1}^{2} r_{2}^{2}}{\pi} \sqrt{\frac{16}{\left(225 	imes 10^{-4}ight)^{2}-\left(25 	imes 10^{-4}ight)^{2}}}$

$=\frac{10 	imes 225 	imes 10^{-4} 	imes 25 	imes 10^{-4} 	imes 4}{\pi 	imes 10^{-4} \sqrt{250 	imes 200}}$

$=\frac{225 	imes 25 	imes 4 	imes 10^{-3}}{\pi 	imes 10^{2} \sqrt{5}}$

$=\frac{45 \sqrt{5}}{\pi} 	imes 10^{-5} \mathrm{m}^{5} / \mathrm{s}=32 \mathrm{ltr} / \mathrm{s}$

Water is flowing through a horizontal tube according to the figure. Its diameter at two points are $0.3\,m$ and $0.1\,m$ respectively. Pressure difference between these two points is equal to $0.8\,m$ of water column. Find rate of flow of water in the tube ..... $ltr/s$

Similar Questions

Water flows through a frictionless duct with a cross-section varying as shown in figure. Pressure $p$ at points along the axis is represented by

A plane is in level flight at constant speed and each of its two wings has an area of $25 \;m ^{2}$ If the speed of the air is $180 \;km / h$ over the lower wing and $234\; km / h$ over the upper wing surface, determine the plane's mass in $kg$. (Take air density to be $1\; kg m ^{-3}$ ).

Water is moving with a speed of $5.0\,m/s$ through a pipe of cross sectional area $4.0\,cm^2$ . The water gradually descends $10\,m$ as the pipe increase in area to $8.0\,cm^2$ . If the pressure at the upper level is $1.5 \times 10^5\,Pa$ , the pressure at lower level will be

Correct Bernoulli's equation is (symbols have their usual meaning) :