$\text {A stratified liquid flows in a $80 - \mathrm { cm }$-wide, 40 -cm-high channel with the density distribution }$$\rho ( y ) = 800 ( 1 + 0.2 y ) \mathrm { kg } / \mathrm { m } ^ { 3 }$ $\text {and a uniform velocity distribution of $1.2 \mathrm {~m} / \mathrm { s }$, with $y$ measured}$$\text { from the bottom of the channel. The mass flux is nearest:}$
A) $260 \mathrm {~kg} / \mathrm { s }$
B) $280 \mathrm {~kg} / \mathrm { s }$
C) $300 \mathrm {~kg} / \mathrm { s }$
D) $320 \mathrm {~kg} / \mathrm { s }$

Question

Quizplus · Accepted Answer

$320 \mathrm {~kg} / \mathrm { s }$
$$\begin{aligned}
\dot { m } = \int _ { A } \rho u d A & = \int _ { 0 } ^ { 0.4 } 800 ( 1 + 0.2 y ) 1.2 \times 0.8 d y \
& = 768 \int _ { 0 } ^ { 0.4 } ( 1 + 0.2 y ) d y = \underline { 319 \mathrm {~kg} / \mathrm { s } }
\end{aligned}$$