Water flowing through a 2.8 cm-diameter pipe can fill a 200 L bathtub in 5.8 min.What is the speed of the water in the pipe?
flowrate=areacrosssection*speed
change 200L to 200dm^3, and the diameter to dm (2.8cm=.28dm)
you don't have to change min to seconds, but I would.
Can you break it down further...if you can
To find the speed of the water in the pipe, we can use the equation:
Speed = Volume / Time
First, let's calculate the volume of water that flows through the pipe in 5.8 minutes. We are given that the bathtub is filled with 200 liters of water, so the volume is 200 liters.
However, the diameter of the pipe is given in centimeters, while the volume is given in liters. We need to convert the diameter from centimeters to meters, as it is a more commonly used unit for flow rate calculations.
The diameter is 2.8 cm, which we can convert to meters by dividing it by 100:
Diameter = 2.8 cm / 100 = 0.028 meters
Now, we can calculate the radius of the pipe, which is equal to half of the diameter:
Radius = 0.028 meters / 2 = 0.014 meters
Next, we need to calculate the cross-sectional area of the pipe using the formula:
Area = π * radius^2
Area = π * (0.014 meters)^2 = 0.0006157 square meters
Now, we can calculate the speed of the water using the equation:
Speed = Volume / Time
Speed = 200 liters / 5.8 minutes
However, we need to convert the volume and time into the corresponding units:
200 liters = 200 * 0.001 cubic meters (1 liter = 0.001 cubic meters) = 0.2 cubic meters
5.8 minutes = 5.8 * 60 seconds (1 minute = 60 seconds) = 348 seconds
Now we can substitute these values into the equation:
Speed = 0.2 cubic meters / 348 seconds
Speed = 0.0005747 cubic meters per second
Therefore, the speed of the water in the pipe is approximately 0.0005747 cubic meters per second.