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am expanding my house and the town is requiring us to increase the size of the water line from the street from 3/4 inch to 1 inch diameter.

intuitively i understand that a bigger pipe results in more volumetric water flow into the house. But i am having trouble figuring out which physics formulas and principles explain why this is both quantitatively and qualitatively.

to simplify the situation lrta assume that the water utility has a 6 inch diameter pipe running down the street with a pressure of 100 psi. then a smaller, 20 foot long pipe heads into my basement. at the end of tis pipe is a valve that i can open to fill up a pool in my basement. everything is horizontal.

in scenario A this smaller pipe is 3/4 inch diameter. in scenario B it is 1 inch diameter.

I can find plenty about bernoullis equation and the continuity principle. But some sources seem to suggest that they are meant to apply to 2 points along the same water stream, not to 2 different scenarios.

so i don't know if they are applicable.

regardless i can sort of grasp that in a larger pipe compared to smaller pipe the water will flow slower but with higher pressure. And i can grasp that flow rate Q = cross sectional area * velocity

so in the larger pipe the cross sectional area is larger and maybe the pressure is higher and the velocity is slower?

But then, if the larger area would tend to lead to a higher Q and a slower velocity to a smaller Q do they balance out and lead to no change in Q?

i also found poisseuiles law which seems to build down to Q being = pressure gradient * A^2

but there again a bigger pipe will increase A but the delta p should decrease due to less friction and bernoullis law. so why does Q change?

plus i am not clear on what the pressure gradient is? when i open the faucet at the end of the pipe wide is the pressure at that end 0 so the delta p is just the pressure at the start of the pipe?

in any event this has been bugging me and it would be great anyone could explain and show me the formula that will calculate the Q, pressure and velocity of the water at that faucet in my basement for scenario A and B

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  • $\begingroup$ the simplest concepts are 1) slower water flow has less pressure loss, and 2) circumference is what leads to friction (pressure loss), but area is the flow, and area increases as a square but circumference increases linearly with diameter. $\endgroup$
    – Tiger Guy
    Oct 2 at 15:15
  • $\begingroup$ Your assumption of a 6 " supply is small from what I have seen. $\endgroup$
    – blacksmith37
    Oct 2 at 16:34
  • $\begingroup$ so to put it all together--- using a larger pipe will tend to increase the flow rate because the diameter/cross sectional area increases. it will tend to decrease the flow rate because the friction and , pressure drop, pressure gradient and velocity are less.But the effect of increasing the flow rate in larger than the effect of decreasing the flow rate, so the flow rate is increased? $\endgroup$
    – Seth Ness
    Oct 3 at 6:34
  • $\begingroup$ bigger pipe passes more water ... you don't really have to make any calculations to confirm that ... just think about what happens to water flow if a second pipe is added ... experience with drinking straws or with garden hoses can also show the relation between pipe size and liquid flow $\endgroup$
    – jsotola
    Oct 3 at 18:20

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If you assume that the mains is a constant pressure source then a bigger pipe is less of a restriction in series with the household pipework therefore allowing more flow to enter the house.

Have a look at this link : Orifice flow

In this example you can assume the mains to be a certain head above the orifice, you should then be able to see the difference in flow following a change in the diameter of the orifice.

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