-
A pipe of 0.7 m diameter has a length of 6 km and connects two reservoirs A and B. The water level in reservoir A is at an elevation 30 m above the water level in reservoir B. Halfway along the pipe line, there is a branch through which water can be supplied to a third reservoir C. The friction factor of the pipe is 0.024. The quantity of water discharged into reservoir C is 0.15 m³/s. Considering the acceleration due to gravity as 9.81 m/s² and neglecting minor losses, the discharge (in m³ /s) into the reservoir B is ______________
-
- 1.985 m³/s
- 2 m³/s
- 2.5 m³/s
- 0.5716 m³/s
Correct Option: D
0.5716
| Friction loss hƒ = | ||
| 2gD |
Q = AV
| ∴ V = | ||
| A |
| A = | D² | |
| 4 |
| = | ||
| 2gπD5 |
Let discharge of reservior A = Q.
Consider lengths 1 and 2.
hƒ1 + hƒ2 = 30 m
| = | + | = 30 | ||
| 2gπ × (7)5 | 2gπ × (7)5 |
| ⇒ | [Q² + (Q - 0.15)²] = 30 | |
| 2 × 9.81 × π × (0.7)5 |
⇒ Q = 0.7216 m³/s
⇒ QB = Q – 0.15 = 0.5716 m³/s
