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?
To find the speed of the water in the pipe, we first need to determine the volume flow rate, which is the volume of water that flows through the pipe per unit of time. We know that a 200 L bathtub can be filled in 5.8 min, so the volume flow rate is:
Volume flow rate = Volume / Time
Volume flow rate = 200 L / 5.8 min
We need to convert the units to be consistent, so we'll convert the volume to cubic meters (m^3) and the time to seconds (s):
1 L = 0.001 m^3
200 L = 200 * 0.001 m^3 = 0.2 m^3
1 min = 60 s
5.8 min = 5.8 * 60 s = 348 s
Now we can find the volume flow rate:
Volume flow rate = 0.2 m^3 / 348 s ≈ 0.000574713 m^3/s
Next, we need to find the cross-sectional area of the pipe. The diameter of the pipe is 2.8 cm, so the radius is half of that, 1.4 cm. We need to convert the radius to meters:
1.4 cm = 1.4 * 0.01 m = 0.014 m
Now we can find the cross-sectional area of the pipe, A, using the formula for the area of a circle:
A = πr^2
A = π(0.014 m)^2 ≈ 0.000615752 m^2
Finally, we can find the speed of the water, v, using the formula:
v = Volume flow rate / Cross-sectional area
v = 0.000574713 m^3/s / 0.000615752 m^2 ≈ 0.933389 m/s
The speed of the water in the pipe is approximately 0.93 m/s.
To find the speed of the water in the pipe, we can use the formula:
Speed = Volume / Time
First, we need to find the volume of water flowing through the pipe. We know that the water can fill a 200 L bathtub in 5.8 minutes.
1 liter (L) = 1000 cm^3
So, the volume of water flowing through the pipe is:
Volume = 200 L * 1000 cm^3/L = 200,000 cm^3
Next, we need to find the cross-sectional area of the pipe. The diameter of the pipe is given as 2.8 cm, so the radius is half of that:
Radius = 2.8 cm / 2 = 1.4 cm = 0.014 m
The cross-sectional area, A, of a pipe can be calculated using the formula:
A = π * r^2
where r is the radius of the pipe. Plugging in the values, we get:
A = π * (0.014 m)^2
Now, we can find the speed of the water by dividing the volume by the cross-sectional area and the time:
Speed = Volume / (A * Time)
Plugging in the values, we have:
Speed = 200,000 cm^3 / (π * (0.014 m)^2 * 5.8 min)
Calculating this expression will give us the speed of the water in the pipe.
To find the speed of the water in the pipe, we need to calculate the volume flow rate. The volume flow rate is the amount of water passing through a section of the pipe per unit of time.
First, let's convert the diameter of the pipe from centimeters to meters. Since 1 meter is equal to 100 centimeters, the diameter of the pipe is 2.8 cm / 100 = 0.028 meters.
Next, we need to calculate the cross-sectional area of the pipe. The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. The radius of the pipe is half of the diameter, so the radius is 0.028 / 2 = 0.014 meters.
Substituting the values into the formula, we get A = π(0.014)^2 ≈ 0.0006157 square meters.
Now, let's calculate the volume flow rate. The volume flow rate is given by the formula Q = A * V, where Q is the volume flow rate, A is the cross-sectional area, and V is the velocity of the water.
We know that the bathtub can hold 200 liters of water, which is equal to 200,000 cubic centimeters or 0.2 cubic meters (1 liter = 1000 cubic centimeters). We also know that it takes 5.8 minutes to fill the bathtub.
Therefore, the volume flow rate can be calculated as Q = 0.2 cubic meters / 5.8 minutes ≈ 0.03448 cubic meters per minute.
Finally, to find the velocity of the water, we divide the volume flow rate by the cross-sectional area: V = Q / A ≈ 0.03448 cubic meters per minute / 0.0006157 square meters ≈ 56.033 meters per minute.
The speed of the water in the pipe is approximately 56.033 meters per minute.