Question regarding pressure equ.

  • Thread starter Thread starter cscott
  • Start date Start date
  • Tags Tags
    Pressure
AI Thread Summary
The discussion centers on the relationship between pressure and height in a water reservoir system, described by the equation ΔP = ρgΔh. When water is released from a hole at the base of a hill, it does not rise to the height of the reservoir due to energy losses from friction and other factors. Static pressure allows water to reach the same elevation if a pipe connects the bottom of the hill to the reservoir. However, when spraying directly, the dynamic conditions prevent the water from achieving the reservoir's height. Ultimately, static conditions are necessary for the water to rise to the reservoir level.
cscott
Messages
778
Reaction score
1
\Delta P = \rho g \Delta h

If my water reservoir for my house is high on a hill I can calculate the pressure at the house if I know the height of the reservoir. If I cut a hole at the base of the hill and let the water spray directly up, will it always rise to the height of the reservoir? I mean, you can use the conservation of energy but I just noticed the equation worked both ways with the same values...
 
Physics news on Phys.org
Yes, but it is static pressure.

If the water sprays, it loses energy from entrance/exit losses as well as friction losses of any pipe and therefore never rise to the same elevation. If you were to run a pipe from the bottom of the hill up to the top of the reservoir, the water would eventually rise to the same elevation under a static condition.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Fluid Dynamics - Using the Manometer Equation
Replies
6
Views
2K
Solving an Air Pressure Question: Who Is Right?
Replies
5
Views
2K
Atmospheric pressure and water pressure - Boyle's law
Replies
6
Views
822
What is the relationship between pressure and flow rate?
Replies
8
Views
4K
How to calculate the velocity of water streaming into the boat?
Replies
19
Views
984
Gauge pressure due to a floating body
Replies
4
Views
2K
Clarifying the Definition Total/Stagnation Pressure (p₀) in Bernoulli'
Replies
2
Views
949
Pressure of water coming out of a hose nozzle
Replies
7
Views
986
A water-bottle demonstration of atmospheric pressure
Replies
6
Views
2K
Hydrostatic pressure at a point inside a water tank that is accelerating
2
Replies
60
Views
6K

Hot Threads

Recent Insights

Back
Top