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Name: Darrin D.
Status: Other
Age: 30s
Location: N/A
Country: N/A
Date: October 2003


Question:
Let us consider that a typical garden hose has 40 psi water running through it. Is it possible to increase water pressure by the type nozzle you use? I mean, couldn't a nozzle say 15 or 20 inches long of smaller diameter than the hose make that pressure stronger? Or maybe the nozzle tip size would make a difference? Basically there is a discussion among co-workers that says a garden hose with a special end could reach up to 600 or 800 psi without any outside influences other that the nozzle tip. Is this possible?



Replies:
According to Bernoulli's equation, which describes the flow of an incompressible, non-viscous fluid during laminar (non-turbulent) flow:

p + dv^2/2 + dgy is constant.

p is the pressure (higher pressure means higher energy per unit volume)
d is the density (kg/m^3), v is the speed of the fluid, y is the height of the fluid.
g is the acceleration due to gravity (9.8 m/s^2 = 32 ft/s^2)
dv^2/2 is the kinetic energy per unit volume
dgy is the gravitational potential energy per unit volume.

Bernoulli's equation is just conservation of energy.

Notice that if the nozzle is of smaller diameter, the velocity of the fluid must increase, since the fluid is incompressible. Then, since the kinetic energy term increases and assuming the height does not change, the pressure must DECREASE.

This is somewhat counterintuitive since a normal nozzle is preceded by a long hose and due to friction with the inner wall of the hose and turbulent flow, the pressure decreases as the water flows though the hose. A smaller nozzle decreases the speed of the water in the hose and so decreases the pressure drop before the nozzle.

However, the speed of the water leaving the nozzle depends only on the pressure and speed of the water in the hose just before the nozzle:
p1 + d*v1^2/2 = patm + d*v2^2
where p1, v1 are the pressure and speed of the water just before the nozzle and patm, v2 are the pressure and speed just after the nozzle. The design of the nozzle cannot change this!

However, if the energy of a large amount of the water can be concentrated on a smaller amount of water, the speed and/or pressure of that smaller amount can be considerably increased. You can buy pumps, called impact pumps I believe, that accomplish that.

Best, Dick Plano...


No, you are not going to increase the pressure. The only way to increase the pressure is to put work into the system. That is why the water pressure cleaners have a pump attached to it to increase the pressure. Just think about the fact that if I were to slowly keep making the nozzle smaller to the point that I cut off the flow, would the pressure increase to infinity? No, the water would stop flowing and a pressure gauge attached to the nozzle would read that 40 psi that is being supplied to the hose. However, what you will change with different nozzles is the velocity of the water leaving the nozzle and the pressure drop out of the nozzle. The continuity equation states that the flow (Q) of water into the hose must equal the flow out, therefore if flow is to remain constant

Qin=Qout

And Q=Area*Velocity

So you can see that if I keep the flow constant but change the area of the nozzle, I must change the velocity to keep the flow constant. So a smaller area means a larger velocity, and a larger velocity means a longer stream of water out of the hose. That is why changing the kind of nozzle type ( or putting your thumb over the opening) results in a different flow pattern. There will be some pressure loss ( i.e. the discharge pressure will be less than 40 psi), but usually that is minimal with larger openings and increases as the area gets smaller.

Thanks for using Newton.

Christopher Murphy, P.E.
Associate Mechanical Engineer


For practical purposes water is incompressible, so neglecting pressure drop due to flow through a hose/pipe, the pressure is "set" by head pressure of a water tower somewhere upstream. The maximum pressure that can be generated would be to close the end of the hose -- the nozzle tip.
Higher pressures, like fire engines need to spray tall buildings are obtained by high pressure pumps that work in a manner (more or less) like the hydraulic lift in a service station in reverse.

Vince Calder



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