Answer to Question #192951 in Mechanics | Relativity for April

Question

Water flows through a venturi meter. At the constricted section where the area is 24 cm2

, the 

pressure is 10.2 N/cm2

, and at the section where the area is 64 cm2

, the pressure is 18.0 N/cm2

. 

Determine the velocities of water in the larger and smaller pipes and the rate of flow. 

Answer 1

Area at section, $A_1=64\space cm^2$

Pressure at section, $P_1=18\space N/cm^2$

Area at constricted section, $A_2=24\space cm^2$

Pressure at constricted section, $P_1=10.2\space N/cm^2$

Density of mercury, $\rho=13.6\space g/cm^3$

Flow rate, $q=\dfrac{A_1A_2}{\sqrt{A_1^2-A_2^2}}\space \sqrt{\dfrac{2(P_1-P_2)}{\rho}}$

$q=\dfrac{64\times24}{\sqrt{64^2-24^2}}\space \sqrt{\dfrac{2(18-10.2)}{13.6}}$

$q=27.72\space cm^3/s$

Velocity at section, $v_1=\dfrac{q}{A_1}=\dfrac{27.72}{64}=0.43\space cm/s$

Velocity at constricted section, $v_2=\dfrac{q}{A_2}=\dfrac{27.72}{24}=1.155\space cm/s$