A swamp containing 4158m³ of water is to be drained by a pump. The pump is connected to a pipe of 7cm and operates 8 hours a day. Water flows through the pipe at a speed of 1.5m per second. Determine the number of days it will take to drain the swamp
First, we need to calculate the flow rate of the pump in m³/s.
The cross-sectional area of the pipe can be calculated using the formula for the area of a circle:
A = πr²
A = π(0.07/2)²
A = π(0.035)²
A = π(0.001225)
A = 0.00385 m²
The flow rate can be calculated as:
Flow rate = speed x area
Flow rate = 1.5m/s x 0.00385m²
Flow rate = 0.005775 m³/s
Now, we can calculate the volume of water drained per day:
Volume drained/day = flow rate x 60 (60 seconds in a minute) x 60 (60 minutes in an hour) x 8 (8 hours/day)
Volume drained/day = 0.005775 m³/s x 60 x 60 x 8
Volume drained/day = 1244.32m³/day
To find the number of days it will take to drain the swamp, we divide the total volume of the swamp by the volume drained per day:
Number of days = 4158m³ / 1244.32m³/day
Number of days = 3.34 days
So, it will take approximately 3.34 days to drain the swamp.