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  • Which one of the following statements is correct? When a fluid passes through the narrow part of nonuniform pipe,Option: 1 its velocity and pressure

Which one of the following statements is correct? When a fluid passes through the narrow part of nonuniform pipe,

Option: 1

its velocity and pressure both increase
 


Option: 2

its velocity and pressure both decrease
 


Option: 3

its velocity decreases but its pressure increases
 


Option: 4

its velocity increases but its pressure decreases


Answers (1)

best_answer

Consider two points A and B in the pipe at the same horizontal level. At point A, let \mathrm{a_1} be the area of cross-section of the pipe, \mathrm{v_1} the velocity of fluid flow and \mathrm{ p_1} the fluid pressure. Let \mathrm{ a_2, v_2} and \mathrm{ p_2} be the corresponding quantities at point B. Then from Bernoulli's theorem, we have

\mathrm{ \begin{gathered} p_1+\frac{1}{2} \rho v_1^2=p_2+\frac{1}{2} \rho v_2^2 \\ \text { or } \quad\left(p_1-p_2\right)=\frac{1}{2} \rho\left(v_2^2-v_1^2\right) \end{gathered} }
If \mathrm{a_2<a_1}, it follows from continuity equation \mathrm{a_1 v_1 =a_2 v_2}, that  \mathrm{v_1>v_2}. From Eq. (i), it follows that \mathrm{p_2<p_1}. Hence, at the narrow part of the pipe, the fluid velocity increases but its pressure decreases,

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Kuldeep Maurya

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