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STD 11 - 9.1 , fluid mechanics — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 9.1 , fluid mechanics4 Marks
MCQ
Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is $P$ at a point where flow speed is $v$ , the pressure at another point where the flow speed is $2v$ , is (Take density of water as $\rho $ )
  • ✓
    $P - \frac{{3\rho {v^2}}}{2}$
  • B
    $P - \frac{{\rho {v^2}}}{2}$
  • C
    $P - \frac{{3\rho {v^2}}}{4}$
  • D
    $P -\rho v^2$
✓

Answer

Correct option: A.
$P - \frac{{3\rho {v^2}}}{2}$
a
Applying Bernoullis's Equation at two points$:$

$p_{1}+\frac{\rho v_{1}^{2}}{2}=p_{2}+\frac{\rho v_{2}^{2}}{2}$

Given, $p_{1}=p, \quad v_{1}=v \quad v_{2}=2 v$

$p_{2}=p+\frac{\rho v^{2}}{2}-\frac{4 \rho v^{2}}{2}$

$p_{2}=p-\frac{3 \rho v^{2}}{2}$

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