Question

A stream function is given by:
$\psi =2x^{2}y+(x+1)y^2$
The flow rate across a line joining points A(3, 0) and B(0, 2) is

• A. 0.4 units
• B. 1.1 units
• C. 4 units
• D. 5 units

Answer 1

The correct option is C 4 units

The rate of flow is the difference in value of stream function at points A and B
$\therefore$ $Q=|{\psi }_A-{\psi }_B|$
${\psi }_A=2\times (3{)}^2\times 0+(3+1)\times (0{)}^2=0$
${\psi }_B=2\times (0{)}^2\times 2+(0+1)\times (2{)}^2=4$
$\therefore$ $Q=|0-4|=4units$