Your green house irrigation sytem is plumbed with 3/4" pvc pipe from which 1/2" branch lines are routed to each row of plants. if the city supplies water that flows at 3ft/sec what is the velocity of the water at plants level? WEhat is the flow rate in gallons per min at plant level?
To determine the rate we need to know the volume/time for a given surface area. The city supplies 3ft^3/sec for 3/4" diameter pipe.
We could use a proportion
r1:A1=r2:A2 where
r1=3, A1= pi*(.75)^2, r2 is what we want, A2= pi*(.5)^2 Thus
r2=r1*A2/A1 = (3*(.75)^2)/(.5)^2 = 3*2.25=6.75 ft^3/sec
You'll need to determine the units yourself. This needs to be converted to gal/min.
Check the arithmetic and the units.
Using the continuity equation assumes all the flow is in the same line (ie, there is one supply line and one branch line). If there are n branch lines, then it becomes..
r1:A1=n*r2:A2 Normally, one would have several branch lines off of the supply line.
I wondered about that after I did it Bob. It seemed to me that branching off should increase the surface area and decrease the flow rate. I am glad that I remembered the basic equation for this kind of problem though.
Thanks for checking this.
To find the velocity of the water at plant level, we can use the principle of continuity. According to the principle of continuity, the flow rate of water remains constant, assuming there are no leaks or blockages in the system.
To calculate the velocity of the water at plant level, we can use the equation:
A1 * V1 = A2 * V2
Where:
A1 = cross-sectional area of the 3/4" diameter pipe
V1 = velocity of water in the 3/4" diameter pipe
A2 = cross-sectional area of the 1/2" branch line
V2 = velocity of water at plant level
The cross-sectional area of a pipe can be calculated using the formula:
A = π * r^2
Let's substitute the given values in the equation:
A1 = π * (0.75/2)^2
A2 = π * (0.5/2)^2
Since we are given that the water flows at 3 ft/sec in the 3/4" diameter pipe, we can substitute these values:
(π * (0.75/2)^2) * 3 = (π * (0.5/2)^2) * V2
Simplifying this equation, we find:
V2 = (π * (0.75/2)^2 * 3) / (π * (0.5/2)^2)
V2 = (0.75/2)^2 * 3 / (0.5/2)^2
V2 = (0.5625 * 3) / 0.25
V2 = 1.6875 / 0.25
V2 = 6.75 ft/sec
Therefore, the velocity of the water at plant level is 6.75 ft/sec.
To calculate the flow rate in gallons per minute at plant level, we can use the equation:
Flow Rate = Velocity * Cross-sectional Area * 7.48 (conversion factor)
The cross-sectional area at plant level can be calculated using the formula:
A = π * (0.5/2)^2
Substituting the given values, we have:
Flow Rate = 6.75 * (π * (0.5/2)^2) * 7.48
Flow Rate = 6.75 * (π * 0.0625) * 7.48
Flow Rate = 6.75 * 0.19634954084936207 * 7.48
Flow Rate ≈ 7.6642 gallons per minute at plant level
Therefore, the flow rate in gallons per minute at plant level is approximately 7.6642.