Question

Two water pipes p and q having diameter 2 into 10 raise to power -2 and 4 into 10 raise to power -2 respectively are joined in series with the main supply line of water .the velocity of water flowing in pipe p is ???????????????????????????????????

Answer 1

Answer on Question # 37158

Physics - Mechanics | Kinematics | Dynamics

Question:

Two water pipes p and q having diameter 2 into 10 raise to power -2 and 4 into 10 raise to power -2 respectively are joined in series with the main supply line of water. the velocity of water flowing in pipe p is ?

Solution:

According to the law of continuity,

$$v _ {1} S _ {1} = v _ {2} S _ {2}.$$

Cross-section area of the pipes p and q are

$$S _ {1} = \frac {\pi d _ {1} ^ {2}}{4}, \qquad S _ {2} = \frac {\pi d _ {2} ^ {2}}{4}$$

respectively. Thus

$$v _ {1} = \frac {v _ {2} S _ {2}}{S _ {1}} = \frac {v _ {2} d _ {2} ^ {2}}{d _ {1} ^ {2}} = v _ {2} \cdot \frac {4 ^ {2}}{2 ^ {2}} = 4 v _ {2}.$$

Answer:

The velocity of water in the pipe p is four times larger than the velocity of water in the pipe q.