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Physics · MECHANICAL PROPERTIES OF FLUIDS
हिन्दीAn incompressible, non-viscous liquid undergoes steady streamline flow through a horizontal tapering pipe. The radius of the cross-section at the entrance is twice that at the exit (\( r_1 = 2 r_2 \)). What is the ratio of the static pressure drop \( (P_1 - P_2) \) along the contraction to the initial dynamic pressure \( (\frac{1}{2}\rho v_1^2) \) at the entrance?
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Correct answer · Option C
\( 15 \)
Explanation
From continuity: \( v_2 = v_1 (\frac{r_1}{r_2})^2 = 4 v_1 \). Pressure drop \( P_1 - P_2 = \frac{1}{2}\rho (v_2^2 - v_1^2) = \frac{1}{2}\rho (16 v_1^2 - v_1^2) = 15 (\frac{1}{2}\rho v_1^2) \). Thus, the ratio is 15.
