A pool has a uniform circular cross section of radius 5 metre and uniform Dept 1.4 metre it is filled by a pipe which delivers water @ 20 litre per second calculate in minutes the time taken to fill the pool.
If the pool is emptied in 42 min by another cylindrical pipe through which water flows at 2 metre per sec , calculate radius of pipe in cm
To calculate the time taken to fill the pool, we first need to find the volume of the pool.
The formula for the volume of a cylinder is given by:
Volume = π * r^2 * h
Where:
- π is a constant approximately equal to 3.14159
- r is the radius of the cylinder (given as 5 meters)
- h is the height or depth of the cylinder (given as 1.4 meters)
Substituting the given values into the formula, we get:
Volume = 3.14159 * (5^2) * 1.4
Volume = 3.14159 * 25 * 1.4
Volume ≈ 109.955 cm^3
Since water is flowing at a rate of 20 liters per second, we can convert this volume into liters.
1 cm^3 = 0.001 liters
So, 109.955 cm^3 ≈ 0.109955 liters
Now, we can find the time taken to fill the pool by dividing the volume by the flow rate:
Time = Volume / Flow rate
Time = 0.109955 liters / 20 liters per second
Time = 0.00549775 seconds
To convert this time into minutes, we can divide it by 60:
Time = 0.00549775 seconds / 60 seconds per minute
Time ≈ 0.00009163 minutes
So, the time taken to fill the pool is approximately 0.00009163 minutes.
Now, let's move on to calculating the radius of the cylindrical pipe.
To calculate the radius of the pipe in cm, we need to consider the given information that the pool is emptied in 42 minutes by another cylindrical pipe through which water flows at 2 meters per second.
We can use the formula for the volume of a cylinder again to find the volume of the pool:
Volume = π * r^2 * h
Where:
- π is a constant approximately equal to 3.14159
- r is the radius of the cylinder (to be calculated)
- h is the height or depth of the cylinder (not given)
We know that the water flows at 2 meters per second, and the pool is emptied in 42 minutes. We need to convert the 42 minutes into seconds by multiplying it by 60:
Time = 42 minutes * 60 seconds per minute
Time = 2520 seconds
Now, we need to find the volume of the pool by multiplying the flow rate (2 meters per second) by the time:
Volume = Flow rate * Time
Volume = 2 meters per second * 2520 seconds
Volume = 5040 cubic meters
Substituting the volume and height values into the volume formula, we can solve for the radius:
5040 = 3.14159 * r^2 * 1.4
r^2 = 5040 / (3.14159 * 1.4)
r^2 ≈ 1208.2469
r ≈ √1208.2469
r ≈ 34.752 cm
So, the radius of the cylindrical pipe is approximately 34.752 cm.