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?
flow rate=volume/time=area*velocity
solve for velocity.
whatch units. I would change L to dm^3, and cm to dm.
can help me by placing numbers cuz its confusing me with words
34.8 min
To find the speed of the water in the pipe, we first need to calculate the volume of water flowing through the pipe per unit time.
Given:
Diameter of the pipe = 2.8 cm
Radius of the pipe = diameter/2 = 2.8 cm/2 = 1.4 cm = 0.014 m (converted to meters)
Formula to calculate the volume of a cylinder:
Volume = π * r^2 * h
where π is the mathematical constant pi (approximately 3.14159), r is the radius of the pipe, and h is the height of the column of water flowing through the pipe.
We need to find the height of the water column (h) that flows through the pipe in 5.8 minutes.
Given:
Volume of water = 200 L (liters)
Time taken = 5.8 min (minutes)
First, convert the volume to cubic meters:
1 L = 0.001 m^3 (conversion factor)
Volume of water = 200 L * 0.001 m^3/L = 0.2 m^3
Now, we can find the height of the water column:
Volume = π * r^2 * h
0.2 = 3.14159 * (0.014^2) * h
Solve for h:
h = 0.2 / (3.14159 * (0.014^2))
h ≈ 55.8196 m
Now, we have the height of the water column (h) in meters.
To find the speed of water, we divide the distance traveled by the time taken.
Distance traveled = π * (r^2) * h
Distance traveled = 3.14159 * (0.014^2) * 55.8196
Distance traveled ≈ 0.109 m
Speed = Distance traveled / Time taken
Speed ≈ 0.109 m / 5.8 min
To convert minutes to seconds:
1 min = 60 seconds
Speed ≈ 0.109 m / (5.8 * 60) s
Speed ≈ 0.00310 m/s
Therefore, the speed of the water in the pipe is approximately 0.00310 m/s.