How can I find the pipe diameter when given the velocity = 1 m/s and the volumetric flow rate = 6000 m^3/day and flow area = 6000 m^2/s

So that everything cancels leaving me with meters so I can write my answer in cm.

To find the pipe diameter, given the velocity, volumetric flow rate and flow area, you can use the equation:

Volumetric flow rate = Velocity × Flow area

First, convert the volumetric flow rate from m^3/day to m^3/s. Since 1 day contains 24 hours and 1 hour contains 3600 seconds, you can divide the volumetric flow rate by 86400 (24 × 3600) to convert it to m^3/s.

6000 m^3/day = 6000 / 86400 m^3/s ≈ 0.0694 m^3/s

Next, rearrange the equation to solve for the flow area:

Flow area = Volumetric flow rate / Velocity

Flow area = 0.0694 m^3/s / 1 m/s = 0.0694 m^2/s

Now, you want to find the pipe diameter in cm. To do this, you need to convert the flow area from m^2/s to cm^2/s. Since 1 m = 100 cm, you can square this conversion factor to convert the area units:

Flow area = 0.0694 m^2/s × (100 cm/m)^2 = 694 cm^2/s

Knowing the flow area, you can calculate the pipe diameter using the formula for the area of a circle:

Flow area = π × (pipe diameter/2)^2

Solving for pipe diameter:

(pipe diameter/2)^2 = Flow area / π

pipe diameter/2 = sqrt(Flow area / π)

pipe diameter = 2 × sqrt(Flow area / π)

pipe diameter = 2 × sqrt(694 cm^2/s / π) = 2 × sqrt(694 cm^2 / π)

Calculating this expression will give you the pipe diameter in centimeters.