Question

The diameters of a pipe at the section 1-1 and 2-2 are 200 mm and 300 mm respectively. If the Velocity of water flowing through pipe at section 1-1 is 4m/s, find: 10 (i) Discharge through the pipe, and (ii) Velocity of water at section 2-2.​

Answer 1

Answer:

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Answer 2

Discharge through the pipe is $0.1256\ m^2/s$ and velocity of water at section 2 is $1.778 m/s$ .

Step 1: Find the water discharge from the pipe.

$\\Given -D_1 = 200mm = 0.2 m\\R_1= \frac{D_1}{2}= 0.1m \\D_2 = 300mm= 0.3 m\\R_2=\frac{D_2}{2}= 0.15m \\ V_1 = 4 m/s\\ V_2 = ?$

Using continuity equation,

$Q = A_1V_1=A_2V_2$

$Q=A_1V_1$

$Q=\pi (0.1)^2$ × $4$

$Q = 0.1256\ m^3/s$

Step 2: Find the velocity of water at section 2.

$Q = A_1V_1=A_2V_2$

= $\pi (R_1)^2$× $V_1$ =  $\pi (R_2)^2$× $V_2$

= $(0.1)^2$× $4$ = $(0.15)^2$× $V_2$

= $0.04 = 0.0225$ × $V_2$

$V_2 = \frac{0.04}{0.0225}$

$V_2 = 1.778 m/s$