I did some math with a few online calculators, and I'm getting varied results:
"40PSI at 1.5" = 110 GPM maximum capacity"
(https://resources.hy-techroof.com/blog/how-much-water-can-flow-through-a-pipe)
ChatGPT spit out this gem:
To determine the flow rate in gallons per minute (GPM), we need to solve for the flow velocity (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow></semantics></math>V) using the Darcy-Weisbach equation and then use the cross-sectional area of the pipe to calculate the flow rate.
Given the parameters provided:
Equivalent length of the pipe (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi></mrow></semantics></math>L): 220 feet
Pipe diameter (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow></semantics></math>D): 0.125 feet (1.5 inches)
Density of water (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ρ</mi></mrow></semantics></math>ρ): 62.4 lb/ft³
Darcy friction factor (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi></mrow></semantics></math>f): 0.02 (assumed)
Pressure drop (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>P</mi></mrow></semantics></math>ΔP) from 40 PSI to atmospheric pressure: 40 PSI - 14.7 PSI = 25.3 PSI
Now, let's plug these values into the Darcy-Weisbach equation to find the flow velocity (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow></semantics></math>V):
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mo>×</mo><mi mathvariant="normal">Δ</mi><mi>P</mi><mo>×</mo><mi>D</mi></mrow><mrow><mi>f</mi><mo>×</mo><mi>L</mi><mo>×</mo><mi>ρ</mi></mrow></mfrac></msqrt></mrow></semantics></math>V=f×L×ρ2×ΔP×D
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mo>×</mo><mn>25.3</mn><mo>×</mo><mn>0.125</mn></mrow><mrow><mn>0.02</mn><mo>×</mo><mn>220</mn><mo>×</mo><mn>62.4</mn></mrow></mfrac></msqrt></mrow></semantics></math>V=0.02×220×62.42×25.3×0.125
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>≈</mo><msqrt><mfrac><mn>6.325</mn><mn>27.456</mn></mfrac></msqrt></mrow></semantics></math>V≈27.4566.325
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>≈</mo><msqrt><mn>0.23</mn></msqrt></mrow></semantics></math>V≈0.23
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>≈</mo><mn>0.479</mn><mtext> </mtext><mtext>ft/s</mtext></mrow></semantics></math>V≈0.479ft/s
Now, we can calculate the flow rate (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow></semantics></math>Q) using the formula:
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mo>=</mo><mi>A</mi><mo>×</mo><mi>V</mi></mrow></semantics></math>Q=A×V
Where <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow></semantics></math>A is the cross-sectional area of the pipe. The cross-sectional area of a pipe with diameter <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow></semantics></math>D is:
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>π</mi><mo>×</mo><msup><mrow><mo fence="true">(</mo><mfrac><mi>D</mi><mn>2</mn></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup></mrow></semantics></math>A=π×(2D)2
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>π</mi><mo>×</mo><msup><mrow><mo fence="true">(</mo><mfrac><mn>0.125</mn><mn>2</mn></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup></mrow></semantics></math>A=π×(20.125)2
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>π</mi><mo>×</mo><mn>0.0625</mn></mrow></semantics></math>A=π×0.0625
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>≈</mo><mn>0.1963</mn><mtext> </mtext><mtext>square feet</mtext></mrow></semantics></math>A≈0.1963square feet
Now, we can calculate the flow rate:
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mo>=</mo><mn>0.1963</mn><mo>×</mo><mn>0.479</mn></mrow></semantics></math>Q=0.1963×0.479
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mo>≈</mo><mn>0.094</mn><mtext> </mtext><mtext>cubic feet per second (cfs)</mtext></mrow></semantics></math>Q≈0.094cubic feet per second (cfs)
To convert cubic feet per second to gallons per minute, we need to multiply by a conversion factor. Since 1 cubic foot per second is approximately 448.831 gallons per minute, we'll use that conversion factor:
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mo>≈</mo><mn>0.094</mn><mo>×</mo><mn>448.831</mn></mrow></semantics></math>Q≈0.094×448.831
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mo>≈</mo><mn>42.285</mn><mtext> </mtext><mtext>GPM</mtext></mrow></semantics></math>Q≈42.285GPM
So, approximately 42.285 gallons per minute will flow from the 1.5" copper pipe at 40 PSI with the given conditions.
Another site had around 85.
We're actually doing this math now, expanding and adding a brewhouse. The engineers are insisting we add a city water buffer tank, as the new house will probably consume more than we can supply (even with a 2" line at like 90psi lol). A buffer tank and a pump may be the way your buddy needs to go too.
------------------------------
Craig Murphy | Plant Manager
Jack's Abby Craft Lagers, Framingham MA
(857) 231-1356
craigm@jacksabby.com------------------------------
Original Message:
Sent: 04-11-2024 14:00
From: Ashton Lewis
Subject: Water Flow Rate Requirement
Hi Craig, they have 40 psig coming into the building.
------------------------------
Ashton Lewis
Manager of Training and Technical Support
BSG Craftbrewing
MBAA District Great Plains, Technical Chair
Springfield, Missouri
(417) 830-2337
------------------------------
Original Message:
Sent: 04-11-2024 12:46
From: Craig Murphy
Subject: Water Flow Rate Requirement
What pressure do you have coming in from the city, in that 1.5" line?
------------------------------
Craig Murphy | Plant Manager
Jack's Abby Craft Lagers, Framingham MA
(857) 231-1356
craigm@jacksabby.com