Question

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, 14 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 discharge into reservoir C is 0.15 m³/s. Considering the acceleration due to gravity as 9.81m/s² and neglecting minor losses, the discharge (in m³/s) into the reservoir B is

Answer 1

The discharge into reservoir B is 0.12 m³/s.

Step-by-step explanation:

To determine the discharge into reservoir B, we can use the continuity equation, which states that the flow rate in two parts of a pipe at the same elevation must be the same. Since the water level in reservoir A is 30 m above the water level in reservoir B, we can use the Bernoulli's equation to calculate the pressure difference between the two reservoirs.

Using the given information, the flow rate from reservoir A to C is 0.15 m³/s. Let's assume the flow rate from reservoir A to B is Q. Since the diameter of the pipe is 0.7 m, the cross-sectional area is (π/4)*(0.7)^2 = 0.385 m². Using the continuity equation, we have (Q/0.385) + (0.15/0.385) = Q. Solving for Q, we get Q = 0.12 m³/s.

Therefore, the discharge into reservoir B is 0.12 m³/s.