Question

Ethanol of density $\rho =700kg/m^3$ flows smoothly through a horizontal pipe that tappers in cross-sectional area from $A_1=1.2\times {10}^{-3}{m}^2$ to $A_2=\frac{A_1}{2}$. The pressure difference between the wide and the narrow sections of pipe is $4200Pa.$ What is the volume flow rate of ethanol in multiples of ${10}^{-4}{m}^3/s$?

• A. $12$
• B. $16$
• C. $24$
• D. None of these

Answer 1

Answer: (C)

$24$

From the equation of continuity,

$A_1{V}_1=A_2{V}_2=\frac{A_1}{2}{V}_2$

$\Rightarrow V_2=2V_1$

From Bernoulli's theorem,

$P_1+\frac{1}{2}\rho V_1^2+\rho gh=P_2+\frac{1}{2}\rho V_2^2+\rho gh$

$\therefore P_1-P_2=\frac{1}{2}\rho (V_2^2-V_1^2)=\frac{1}{2}\rho \times 3V_1^2$

$\therefore 4200=\frac{1}{2}\times 700\times 3V_1^2$

$\Rightarrow V_1=2m{s}^{-1}$

Volume flow rate of Ethanol is: $R=A_1{V}_1=1.2\times {10}^{-3}\times 2m^3{s}^{-1}=24\times {10}^{-4}{m}^3{s}^{-1}$

$\therefore$ R is 24 in multiples of ${10}^{-4}{m}^3{s}^{-1}$