A pipe A is connected with other pipes B and C as shown in the figure. The areas of cross-section of A, B and C are respectively $α, \frac{α}{2}$ and $\frac{α}{4}$ . If the velocities of flow of water through A and B are $10$ m/sec and $6$ m/sec, respectively, then velocity of flow, $V_{c}$ along C is

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TestHub · Accepted Answer

According to the principle of continuity, the total volume of fluid entering a junction per unit time must equal the total volume of fluid leaving the junction per unit time.

Therefore, the rate of flow of water through pipe A is equal to the sum of the rates of flow through pipes B and C:

$A_{A} V_{A} = A_{B} V_{B} + A_{C} V_{C}$

Given the cross-sectional areas and velocities:
$A_{A} = α$ , $V_{A} = 10$ m/s
$A_{B} = \frac{α}{2}$ , $V_{B} = 6$ m/s
$A_{C} = \frac{α}{4}$ , $V_{C} = ?$

Substituting these values into the continuity equation:

$α \times 10 = (\frac{α}{2}) \times 6 + (\frac{α}{4}) \times V_{C}$

$10 α = 3 α + \frac{α}{4} V_{C}$

$7 α = \frac{α}{4} V_{C}$

$V_{C} = 7 \times 4 = 28$ m/s

Thus, the velocity of flow along C is $28$ m/sec.

Answer: $28$ m/sec

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