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  • Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is v, what is the pressure at another point wher

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is v, what is the pressure at another point where the velocity of flow is \mathrm{2 v ; \rho} being the density of water?

Option: 1

\mathrm{p-\frac{3}{2} \rho v^2}


Option: 2

\mathrm{p+\frac{3}{2} \rho v^2}


Option: 3

\mathrm{p-2 \rho v^2}


Option: 4

\mathrm{p+2 \rho v^2}


Answers (1)

best_answer

According to Bernoulli's theorem, for a horizontal flow at a height h from ground level,

\mathrm{p_1+\frac{1}{2} \rho v_1^2+\rho g h=p_2+\frac{1}{2} \rho v_2^2+\rho g h}

\mathrm{or\, \, \, \, \, \, \, \, p_2=p_1+\frac{1}{2} \rho\left(v_1^2-v_2^2\right) }

                    \mathrm{\begin{aligned} & =p+\frac{1}{2} \rho\left\{v^2-(2 v)^2\right\} \\\\ & =p-\frac{3}{2} \rho v^2 \end{aligned}}

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Nehul

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