Q 11-09-092JEE MainJEE Main 2023 (12 Apr, Shift 1)Medium
Glycerin of density $1.25\times10^3\ \text{kg m}^{-3}$ is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are $10\ \text{cm}^2$ and $5\ \text{cm}^2$ and pressure drop across its length is $3\ \text{N m}^{-2}$. The rate of flow of glycerin through the pipe is $x\times10^{-5}\ \text{m}^3\ \text{s}^{-1}$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 4
Bernoulli and continuity: $\Delta P=\tfrac12\rho Q^2\left(\dfrac1{A_2^2}-\dfrac1{A_1^2}\right)$.
$$Q=A_1A_2\sqrt{\frac{2\Delta P}{\rho(A_1^2-A_2^2)}}=5\times10^{-7}\sqrt{\frac{6}{1250\times0.75\times10^{-6}}}=5\times10^{-7}\times80=4\times10^{-5}\ \text{m}^3\ \text{s}^{-1}$$
Solution by Sreeraj P, M.Sc Physics