Question regarding flow rate?

[PhyIsOhSoHard]

Homework Statement

Water from a faucet flows into a glass on a balance. The balance reacts quickly and the reading is increasing steadily. If the water flow is stopped suddently, how will the balance reading change compared to a reading just before the stop? Will the balance reading increase? Decrease? Or not change?

Attempt at an solution
Apparently the correct answer is that the balance reading will decrease. But why? I don't get it?

 

[tiny-tim]

Hi PhyIsOhSoHard!

Hint: force = rate of change of momentum …

what is causing the momentum to change? ​

 

[PhyIsOhSoHard]

Hi PhyIsOhSoHard!

Hint: force = rate of change of momentum …

what is causing the momentum to change? ​

Hi!

I really have no idea. Gravitational force?

 

[tiny-tim]

when the water comes out of the faucet, it has momentum

as it falls, that momentum even becomes slightly more (because of gravity)

after that, what causes that momentum to change?​

 

[PhyIsOhSoHard]

when the water comes out of the faucet, it has momentum

as it falls, that momentum even becomes slightly more (because of gravity)

after that, what causes that momentum to change?​

Hmm, Newton's 3rd law? Cause it hits the water already in the glass, and that water hits back?

 

[tiny-tim]

Hmm, Newton's 3rd law? Cause it hits the water already in the glass, and that water hits back?

yeees …

do you think you could use a physics word, rather than "hits"?

 

[PhyIsOhSoHard]

yeees …

do you think you could use a physics word, rather than "hits"?

Penetrates? Contacts? It does actions and the other does reactions? :(

 

[tiny-tim]

has your professor covered force yet?

 

[PhyIsOhSoHard]

has your professor covered force yet?

Ohhh, you mean momentum as in this?
$\vec{F}=\vec{F_S}+\vec{F_B}=\frac{\partial}{\partial t}\int_{CV}\vec{V}\rho d∀+\int_{CS}\vec{V}\rho\vec{V}\cdot\vec{A}$

So we have a control volume that is the water inside the glass.
If we assume steady flow then the flow is not dependent of time. Our body force is the gravitational force and we have no pressures to account for on the surface.
So on our control surface we have $\vec{Mg}_y=\int_{CS}\vec{V}\rho\vec{V}\cdot\vec{A}$ and we can neglect density if we assume incompressible fluid so that leaves with the momentum:

$\vec{Mg}_y=\int_{CS}\vec{V}\vec{V}\cdot\vec{A}$

But how can you conclude a decrease in the reading based on that? Is it possible?

 

[tiny-tim]

"control volume"? "control surface"?

are you majoring in engineering? ​

let's keep this simple …

at any instant, there are three bodies:
i] the falling water
ii] the water in the glass (and the glass itself)
iii] the scale

do three free body diagrams, for each of the three bodies …

where does the force come from that stops the falling water?​

 

[PhyIsOhSoHard]

"control volume"? "control surface"?

are you majoring in engineering? ​

let's keep this simple …

at any instant, there are three bodies:
i] the falling water
ii] the water in the glass (and the glass itself)
iii] the scale

do three free body diagrams, for each of the three bodies …

where does the force come from that stops the falling water?​

Ya, this is for my fluid mechanics class. I was just hoping there were some of the equations in the chapter that could explain the phenomenon and since the equation is called momentum in my book, I thought maybe that was it lol

i] We have a force down
ii] The water in the glass exerts a reaction force (parallel and opposite in direction to the force coming from the water faucet
iii] The scale exerts a normal force

So as the water from the faucet flows into the glass, we have an equilibrium. When the water from the faucet suddenly stops, the equilibrium is broken and we have an acceleration (momentum) and a net force pointing upwards and since the acceleration by Newton's second law is defined as force divided by mass, the mass of the water inside the glass moves in the same direction as the acceleration (upwards parallel with the reaction force from ii]) and thus the reading will decrease for a very quick moment because of the mass moving upwards at that instant?

 

[tiny-tim]

So as the water from the faucet flows into the glass, we have an equilibrium. When the water from the faucet suddenly stops, the equilibrium is broken and we have an acceleration (momentum) and a net force pointing upwards and since the acceleration by Newton's second law is defined as force divided by mass, the mass of the water inside the glass moves in the same direction as the acceleration (upwards parallel with the reaction force from ii]) and thus the reading will decrease for a very quick moment because of the mass moving upwards at that instant?

are you talking about the moment the faucet is turned off?

if so, you have a strange idea of what "equilibrium" is

i'm asking about the forces while the water is still flowing …

while the faucet is still on, what stops the falling water from falling?

(and you might want to mention the spring inside the scale, the one that's attached to the pointer )

 

[PhyIsOhSoHard]

are you talking about the moment the faucet is turned off?

if so, you have a strange idea of what "equilibrium" is

i'm asking about the forces while the water is still flowing …

while the faucet is still on, what stops the falling water from falling?

(and you might want to mention the spring inside the scale, the one that's attached to the pointer )

Oh yeah. If the acceleration is constant then there's still equilibrium right? :)

You mean the normal force that the glass and balance exerts on the water?

 

[tiny-tim]

how about the spring and the pointer?

what makes the pointer move?