Answer to Question #149092 in Math for Usman

Question

The diameter of a pipe at the section 1 and 2 are 15 cm and 20 cm respectively. Find the discharge through the pipe if velocity of water at section 1 is 4 m/s. Determine also the velocity at section 2.

Answer 1

Diameter of pipe 1 $d_1=15 cm=0.15\ m$

C/S Area of pipe 1 $A_1 =\dfrac{\pi(d_1)^2}{4}=0.005625\pi\ m^2$

Diameter of pipe 2 $d_2=20\ cm=0.2\ m$

C/S Area of pipe 2 $A_2 =\dfrac{\pi(d_1)^2}{4}=0.01\pi\ m^2$

Velocity at pipe 1 $v_1=4\ m/s$

Velocity at pipe 2 $v_2=?$

Discharge through pipe 1 $Q_1=A_1v_1=0.005625\pi\ m^2 (4\ m/s)$

$=0.0225\pi\ m^3/s=0.0707\ m^3/s$

$Q_1=0.0707\ m^3/s$

From continuity $Q_1=Q_2+Q_3$

Discharge through pipe 2 $Q_2=A_2v_2=0.01\pi\ m^2 (v_2)$

$=Q_1=0.0225\pi\ m^3/s$

Velocity at pipe 2 $v_2=\dfrac{Q_2}{A_2}=\dfrac{0.0225\pi\ m^3/s}{0.01\pi\ m^2 }=2.25\ m/s$

$v_2=2.25\ m/s$