Can flow rate (or pressure) at the end increase if the diameter of pipe increased and then gradually reduced along the way?

Question

We have a water tank that's just 6.5 - 7 ft above ground level. The length of the pipe from water tank to sink tap would be around 25 ft. Output from water tank is an 1.5 inch pipe which then reduced to 1 inch pipe after 5 ft. Then the remaining 20 ft (1 inch pipe) is connected to sink tap which then finally reduced to 0.5 inch as per sink tap size. Sink tap is 3 ft above ground level. Due to the lower tank height and thus lesser gravitational pressure (???), the flow rate (also pressure ?) in the sink tap is not optimal (or I could say it's bit below usual flow rate). So plumber is considering following strategies to increase the flow rate (pressure ?) at the sink tap.

Increase the tank height further 3 ft (10 ft above ground level)

Starting 10 ft length would be covered by 1.5 inch pipe

Reduce from 1.5 inch to 1.25 inch after 10 ft

Next 10 ft length would be covered by 1.25 inch pipe

Reduce from 1.25 inch to 1 inch after that

Remaining 5 ft length would be covered by 1 inch pipe

Finally the 1 inch pipe is reduced to 0.5 inch at the sink tap connection

Obviously increasing the tank height would increase the flow rate (due to increased pressure), but does gradually reducing the pipe size (3 times) along the way increases the flow rate (pressure ?) at the end (sink tap) than what it was before?

blacksmith37 · Answer

Simple answer : any reduction in diameter at any location will potentially reduce flow and/or pressure, depending on the volume of fluid. With a low volume ,it will make no difference. With a high ( potential) volume ,it will be reduced.

Answered by blacksmith37 on November 12, 2021

Jim Stewart · Answer

Reducing the pipe diameter progressively would not increase the pressure nor flow rate at the tap. The idea is based on a nozzle at the end of a hose giving rise to a high speed jet of water. The nozzle actually reduces the flow rate (volume/time) through the hose and so increases the pressure just before the nozzle. This gives a higher velocity stream but lower flow rate. I assume what you want is a higher flow rate from your faucet.
Notice: I think I am right on my claim in the above, but frankly I am not sure. See edit below*.
You would get a higher flow rate from the faucet if you remove (unscrew) the aerator on the end of the faucet. This is a flow restrictor. Increasing the head would also increase pressure and flow rate.
*EDIT
The most basic formula for laminar (smooth) flow of water in a circular cross section pipe is Poiseuille's equation. To paraphrase, this states that the volume flow rate for an incompressible fluid is equal to the applied pressure times the cross sectional area of the pipe divided by (the length of the pipe times viscosity times 8). This means that progressively decreasing the diameter of the pipe would decrease flow and not increase it.

Can flow rate (or pressure) at the end increase if the diameter of pipe increased and then gradually reduced along the way?

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