A rectangular reservoir is 120m long,and 75cm wide .at what speed per hour must water flow into it through a square pipe of 20cm wide so that the water rises by2.4m in 18hrs.
To determine the speed at which water must flow into the rectangular reservoir, we can use the equation for flow rate:
Flow Rate = Area * Velocity
In this case, the area would be the cross-sectional area of the square pipe, and the velocity would be the speed of the water flow.
Step 1: Convert the measurements to the same unit
The reservoir is 120m long and 75cm wide. To make the calculations easier, let's convert the width to meters:
Width = 75 cm = 75/100 m = 0.75 m
Step 2: Calculate the cross-sectional area of the pipe
The pipe is square, so its cross-sectional area is equal to the side length squared:
Pipe Area = (Side Length)^2 = (0.2 m)^2 = 0.04 m^2
Step 3: Calculate the volume of water that flows into the reservoir
To calculate the volume, we need to multiply the cross-sectional area of the pipe by the height that the water rises in the reservoir:
Volume = Pipe Area * Height = 0.04 m^2 * 2.4 m
Step 4: Calculate the flow rate
The flow rate equals the volume divided by the time:
Flow Rate = Volume / Time = (0.04 m^2 * 2.4 m) / 18 hrs
Step 5: Convert the time to seconds
Since the speed is usually expressed in meters per second, let's convert the time from hours to seconds:
Time = 18 hrs = 18 * 60 * 60 sec = 64800 sec
Step 6: Calculate the flow rate
Now that we have the volume and time in the appropriate units, we can calculate the flow rate:
Flow Rate = (0.04 m^2 * 2.4 m) / 64800 sec
Simplifying the equation, we get:
Flow Rate = 0.000096 m^3/sec
Step 7: Calculate the speed of water flow
Since the flow rate is equal to the product of the area and the velocity, we can rearrange the equation to solve for velocity:
Velocity = Flow Rate / Area = 0.000096 m^3/sec / 0.04 m^2
Simplifying the equation, we get:
Velocity = 0.0024 m/sec
Therefore, the water must flow into the reservoir through the square pipe at a speed of 0.0024 meters per second (or 2.4 m/s).
to rise by 2.4m in 18 hours, the volume must increase by
120*.75*2.4 = 216 m^3/hr
the square pipe has cross-section area of .2^2 = .04 m^2
216 m^3/hr / .04m^2 = 5400 m/hr