Question

Daniel's good friend Giovanni Venturi joined him for another round of fraps. They were discussing ways to determine the velocity of water in a pipe. If the pressure drops 650 kPa as water flowing in a 31 cm diameter pipe is forced to flow through a 19 cm diameter portion, what is the velocity of the water in the 31 cm section of pipe?

Answer 1

Answer:

Explanation:

Given

Pressure drop $\Delta P=650\ kPa$

inlet diameter $d_1=31\ cm$

Outlet diameter $d_2=19\ cm$

density of water $\rho=10^3\ kg/m^3$

Suppose $v_1$ and $v_2$ be the inlet and outlet velocity

According to continuity equation

$A_1v_1=A_2v_2$

where A=cross-section of Pipe

$A=\frac{\pi d^2}{4}$

thus $d_1^2v_1=d_2^2v_2$

$v_2=v_1\times (\frac{d_1}{d_2})^2$

$v_2=v_1\times (\frac{31}{19})^2$

Also from Bernoulli's Equation

$\Delta P=\frac{1}{2}\rho (v_2^2-v_1^2)$

$650\times 10^3=\frac{1}{2}\times 10^3\times (v_1^2(\frac{31}{19})^4-v_1^2)$

$v_1=\sqrt{106.79}$

$v_1=10.33\ m/s$