Q 11-09-124JEE MainJEE Main 2020 (9 Jan, Shift 1)Medium
Water flows in a horizontal tube. The pressure of water changes by $700$ N m$^{-2}$ between $A$ and $B$ where the areas of cross section are $40$ cm$^2$ and $20$ cm$^2$, respectively. Find the rate of flow of water through the tube. (density of water $= 1000$ kg m$^{-3}$)
Answer: (B) $2720$ cm$^3$/s
Continuity: $A_Av_A = A_Bv_B$, so $v_B = 2v_A$.
Bernoulli for a horizontal tube:
$$P_A - P_B = \frac{1}{2}\rho(v_B^2 - v_A^2) = \frac{1}{2}(1000)(3v_A^2) = 1500\,v_A^2$$
$$1500\,v_A^2 = 700 \Rightarrow v_A = 0.683\ \text{m/s}$$
Rate of flow $= A_Av_A = 40\times10^{-4}\times0.683 = 2.73\times10^{-3}\ \text{m}^3/\text{s} \approx 2720\ \text{cm}^3/\text{s}$.
Solution by Sreeraj P, M.Sc Physics