Question

Water flows through a horizontal tube of variable cross section. The area of cross section at A and B are 4 mm² and 2 mm² respectively. If 1 cc of water enters per second through A, find the speed of water at B?

• A. 25 cm/s
• B. 50 cm/s
• C. 25 mm/s
• D. 50 mm/s

Answer 1

The correct option is B

50 cm/s

Given 1 $c{m}^3$ of water enters per second through A
$\Rightarrow A_1{V}_1=1$$\frac{c{m}^3}{s}$
Taking Area in $c{m}^2$ and velocity in $\frac{cm}{s}$
Also, Area of cross section at A = 4 $m{m}^2$
1cm=10mm
$\Rightarrow 4m{m}^2=\frac{4}{100}c{m}^2$
$\frac{4}{100}\times V_A=1$
$\Rightarrow V_A=\frac{100}{4}=25\frac{cm}{s}$
Also from equation of continuity,
$A_A{V}_A=A_B{V}_B$
$\frac{4}{100}\times 25=\frac{2}{100}\times V_B$
$V_B=50\frac{cm}{s}$