# Can Anyone Explain This? (Conservation of momentum) **URL:** \ **Category:** Factual Questions\ **Created:** [May 5, 2012, 4:36pm UTC](https://boards.straightdope.com/t/can-anyone-explain-this-conservation-of-momentum/621003 "2012-05-05T16:36:07Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![ralph124c](https://avatars.discourse-cdn.com/v4/letter/r/8797f3/32.png) [@ralph124c](https://boards.straightdope.com/u/ralph124c)\ **Post date:** [May 5, 2012, 4:36pm UTC](https://boards.straightdope.com/t/can-anyone-explain-this-conservation-of-momentum/621003/1 "2012-05-05T16:36:07Z")
I have a kitchen sink faucet that incorporates the sprayer in the head. You can switch the flow from stream to shower-like. I have noticed something odd-when the switch is set to “stream”-the head doesn’t jerk back, when you turn the water flow on. In contrast, the “spray” mode provokes a noticable snap back. Why would thyere be any difference? In spray mode, the water is forced through a smaller aperture-so the water velocity increases-but the volume/mass is reduced as well. Shouldn’t both streams have the same momemntum (m x v)? ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [May 5, 2012, 5:36pm UTC](https://boards.straightdope.com/t/can-anyone-explain-this-conservation-of-momentum/621003/2 "2012-05-05T17:36:01Z")
> [@ralph124c](#): > > but the volume/mass is reduced as well. What makes you say that? I doubt that’s true. To test it, get a stopwatch and a pitcher. Fill it up in both ways and see if there’s any difference in time. If not, then you’re not actually getting any less volume, as you allege. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [May 5, 2012, 5:54pm UTC](https://boards.straightdope.com/t/can-anyone-explain-this-conservation-of-momentum/621003/3 "2012-05-05T17:54:25Z")
For a stream of flowing water, the thrust is proportional to the momentum flow rate: p-dot = m-dot \* V where p-dot = momentum flow rate m-dot = mass flow rate V = fluid velocity But, m-dot = rho \* V \* A where A = total flow area rho = density So, p-dot = rho \* V^2 \* A From fluid mechanics, the velocity of flow through an orifice (neglecting discharge coefficient) is V = sqrt(2\*P/rho) where P = pressure just upstream of the nozzle So, p-dot = rho \* sqrt(2\*P/rho)^2 \* A or, **p-dot = 2_P_A** So two main factors can be different in each spray configuration: the total spray flow area, or the pressure just inside the nozzle. If the nozzle flow area of one configuration is much greater, then the flow rate will also be much greater; this can result in pressure drop in the supply such that the pressure _just_ upstream of the nozzle ends up being lower. The magnitude of that change in pressure is dependent on the specifics of your supply: the restriction in the faucet valve, the hose to the sprayer head, the details of the flow passages in the spray head. Hard to say how much the pressure will drop with increasing flow in your specific system, without doing some testing. Bottom line, it’s not surprising that different flow configurations will result in different levels of thrust. [sub]…someone check my math…[/sub] ---
**Author:** ![enipla](https://avatars.discourse-cdn.com/v4/letter/e/54ee81/32.png) [@enipla](https://boards.straightdope.com/u/enipla)\ **Post date:** [May 6, 2012, 1:05pm UTC](https://boards.straightdope.com/t/can-anyone-explain-this-conservation-of-momentum/621003/4 "2012-05-06T13:05:05Z")
I would guess that the ‘shower’ mode is not aerated. But the ‘stream’ is. Perhaps the addition of air is the factor not considered. ---
**Author:** ![ralph124c](https://avatars.discourse-cdn.com/v4/letter/r/8797f3/32.png) [@ralph124c](https://boards.straightdope.com/u/ralph124c)\ **Post date:** [May 6, 2012, 4:13pm UTC](https://boards.straightdope.com/t/can-anyone-explain-this-conservation-of-momentum/621003/5 "2012-05-06T16:13:04Z")
> [@Machine\_Elf](#): > > For a stream of flowing water, the thrust is proportional to the momentum flow rate: > > p-dot = m-dot \* V > > where p-dot = momentum flow rate > m-dot = mass flow rate > V = fluid velocity > > But, m-dot = rho \* V \* A > where A = total flow area > rho = density > > So, > > p-dot = rho \* V^2 \* A > > From fluid mechanics, the velocity of flow through an orifice (neglecting discharge coefficient) is > > V = sqrt(2\*P/rho) > > where P = pressure just upstream of the nozzle > > So, p-dot = rho \* sqrt(2\*P/rho)^2 \* A > > or, **p-dot = 2_P_A** > So two main factors can be different in each spray configuration: the total spray flow area, or the pressure just inside the nozzle. If the nozzle flow area of one configuration is much greater, then the flow rate will also be much greater; this can result in pressure drop in the supply such that the pressure _just_ upstream of the nozzle ends up being lower. The magnitude of that change in pressure is dependent on the specifics of your supply: the restriction in the faucet valve, the hose to the sprayer head, the details of the flow passages in the spray head. Hard to say how much the pressure will drop with increasing flow in your specific system, without doing some testing. Bottom line, it’s not surprising that different flow configurations will result in different levels of thrust. > > [sub]…someone check my math…[/sub] Thanks for explaining this. I just thought that the momentum would be the same for both configurations-obviously that is not the case ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [May 6, 2012, 4:15pm UTC](https://boards.straightdope.com/t/can-anyone-explain-this-conservation-of-momentum/621003/6 "2012-05-06T16:15:28Z")
Moved MPSIMS --\> GQ.