Bernoulli's Principle Problem/Energy Conservation

[erinfalk]

Homework Statement

Hi! The problem states: Water through a certain sprinkler system flows trhough a level hose connected to a nozzle which is directed directly upwards. The water leaves the nozzle and shoots to a height, h, before falling back down again into a pool.
The hose is connected to a reservoir which maintains the water there at a pressure, P_res Assume no viscosity of flow, until water exits the nozzle. Use the following notation:
A_noz= cross sectional area of nozzle
L_hose=length of hose
P_atm=atmospheric pressure
ρ=density of water

What is the best expression for the velocity of the water just after it leaves the nozzle? (A)
What is the best expression for the height, h? (B)

Homework Equations

Bernoulli's equation, and conservation of energy (Initial kinetic energy of water=final potential energy of water at height, h)

The Attempt at a Solution

So, I actually was fine on the calculation of this problem, but I am having difficulty understanding the rationale behind (A). I calculated V_exit= (2[(P_res-P_atm)/ρ])^(1/2)
However, to do this, I ignored the velocity of the water in the reservoir. That makes sense, it is hardly moving compared to the velocity of the novel because the regions have equal flow rates. However, I also ignored the ρgh term for the water in the reservior. I guess that I am confused as to why this term doesn't have to be taken into account.

If anyone could explain, that would be great!

 

[sankalpmittal]

Homework Statement

Hi! The problem states: Water through a certain sprinkler system flows trhough a level hose connected to a nozzle which is directed directly upwards. The water leaves the nozzle and shoots to a height, h, before falling back down again into a pool.
The hose is connected to a reservoir which maintains the water there at a pressure, P_res Assume no viscosity of flow, until water exits the nozzle. Use the following notation:
A_noz= cross sectional area of nozzle
L_hose=length of hose
P_atm=atmospheric pressure
ρ=density of water

What is the best expression for the velocity of the water just after it leaves the nozzle? (A)
What is the best expression for the height, h? (B)

Homework Equations

Bernoulli's equation, and conservation of energy (Initial kinetic energy of water=final potential energy of water at height, h)

The Attempt at a Solution

So, I actually was fine on the calculation of this problem, but I am having difficulty understanding the rationale behind (A). I calculated V_exit= (2[(P_res-P_atm)/ρ])^(1/2)
However, to do this, I ignored the velocity of the water in the reservoir. That makes sense, it is hardly moving compared to the velocity of the novel because the regions have equal flow rates. However, I also ignored the ρgh term for the water in the reservior. I guess that I am confused as to why this term doesn't have to be taken into account.

If anyone could explain, that would be great!

Can you draw the diagram of the problem please ? Looks like you are confused with wordings.

 

[rude man]

However, I also ignored the ρgh term for the water in the reservior. I guess that I am confused as to why this term doesn't have to be taken into account.

If anyone could explain, that would be great!

Homework Statement

You were given the pressure in the reservoir at the point where the hose connects to it. So there is no change in potential energyfrom that point until the water squirts out of the nozzle & climbs.

Had the problem stated 'the hose is connected to a point h below the surface of the water', then you would have had to use p = p_atm + rho g h. The result would have been the same.

The problem statement did not make clear whether p_res included p_atm. You might want to check on that.