Water flowing through a 2.8 cm-diameter pipe can fill a 200 L bathtub in 5.8 min.
Flow rate Q = volume/time = speed * cross section area
Q=200/5.8=speed*.028....i get 1231.52
or
Q=(200/348)=speed*.028...i get 20.52
both are wrong so what do i do?
crosssection area of a pipe is not the diameter. It is PI(diameter/2)^2
but besides that, you need to change Liters to a dimension cubed.
I think working in decimeters^3 will be best.
200dm^3=speed*PI(diameter/2)
=speed*PI(.25dm/2)^2
speed=200/(PI*.125^2) in dm/sec
Think that out, why it is right.
ok so i did speed=200/(pi*.25^2) ...i got 3.97 which is wrong
maybe because i have to get the answer in m/s
To find the flow rate Q, you need to divide the volume of water (200 L) by the time it takes to fill the bathtub (5.8 min). It seems like you have correctly calculated the flow rate, which is approximately 34.48 L/min. However, your confusion lies in determining the speed of water.
To calculate the speed, you can rearrange the formula Q = speed * cross-sectional area. In this case, the cross-sectional area is the area of the pipe. The formula for the area of a circle is A = π*r^2, where r is the radius of the pipe.
Given that the diameter of the pipe is 2.8 cm, you can calculate the radius by dividing the diameter by 2: r = 2.8 cm / 2 = 1.4 cm.
Now, convert the radius from cm to meters by dividing by 100: r = 1.4 cm / 100 = 0.014 meters.
Now, substitute the radius into the formula for the area of a circle: A = π * (0.014 meters)^2 ≈ 0.0006157 square meters.
Next, rearrange the formula Q = speed * cross-sectional area to solve for the speed: speed = Q / cross-sectional area.
Substituting the known values: speed = 34.48 L/min / 0.0006157 square meters.
Now, convert the flow rate from L/min to m^3/s: 34.48 L/min × (1 m^3 / 1000 L) × (1 min / 60 s) ≈ 0.0005747 m^3/s.
Plugging in the values: speed = 0.0005747 m^3/s / 0.0006157 square meters ≈ 0.933 m/s.
Therefore, the speed of water flowing through the pipe is approximately 0.933 m/s.