Question

Consider the following velocity profiles in pipline:




Among these profiles, the momentum correction factor would be

• A. Least in 4
• B. Highest in 1
• C. More in 3 than that for 2
• D. The same in 1, 2, 3 and 4

Answer 1

The correct option is C More in 3 than that for 2

More uniform flow gives less moment correction factor.

The average velocity in all the cases is V. The momentum correction factor is defined as

$\beta =\frac{1}{A}\int {\left(\frac{v}{V}\right)}^{2}dA=\frac{1}{D}{\int }_0^D{\left(\frac{v}{V}\right)}^{2}dy$

$\text{Figure}1:{\beta }_1=1.0$

$\text{Figure}2:{\beta }_2=\frac{2}{D}{\int }_0^{\frac{D}{2}}{\left(\frac{1.25v-0.5v\frac{y}{D}}{V}\right)}^{2}dy$

$=2{\int }_0^{\frac{1}{2}}{(1.25-0.5\frac{y}{D})}^{2}d\left(\frac{d}{D}\right)$

$=1.27$

$\text{Figure}3:{\beta }_3=2{\int }_0^{\frac{1}{2}}{(1.5-\frac{y}{D})}^{2}d\left(\frac{y}{D}\right)$

$=1.583$

$\text{Figure}4:{\beta }_4=2{\int }_0^{\frac{1}{2}}{(2-2\frac{y}{D})}^{2}d\left(\frac{y}{D}\right)$

$=2.33$

$\text{Thus}{\beta }_1<{\beta }_2<{\beta }_3<{\beta }_4$