Energy Conservation Flashcards
The principle of energy conservation for fluids is captured by the Bernouilli equation. What is it?
E (energy density) = constant along streamline
E = p + rho(g)(z) + 1/2 rho (U^2)
What are the assumptions made when using the steady Bernouilli equation?
- steady flow
- constant density flow
- dissipationless flow
Why is it useful to work in terms of heads for liquids?
- Head has unit of length ie. m
- This means that the pressure head represents the column of fluid required to produce the pressure p
What is the piezometric head?
Pressure head p/rho(g) + Elevation head z
Can be seen as the total potential energy of the flow
Constant in the vertical when the pressure variation is hydrostatic
What are the energy grade line and the hydraulic grade line?
The EGL and HGL are graphical representations of the energy state of the fluid along a streamline
energy state ie. total head H/ piezo head h
How is the second Bernouilli equation used?
The 2nd Bernouilli equation provides important info about pressure in a fluid body.
It implies pressure across straight streamlines is constant in a horizontal plane
And by including gravity, piezometric head across straight streamlines is constant
This can be extended to the case when the fluid is in free fall (for ‘weightless’ fluid, where streamlines are just horizontally straight)
When can or can’t Bernouilli’s equation be used?
Can:
- converging streamlines
- accelerating fluid
- low energy losses
Cannot:
- diverging streamlines
- decelerating fluid
- turbulence: energy losses
For draining reservoirs, what is the draining velocity dependent on?
The velocity is dependent on the distance to the free surface
U = (2gh)^0.5
What is the stagnation point?
Point at which fluid flow impinges solid surface and has equal probability of moving up or down thereafter
What is another term for the kinetic energy per unit volume?
Dynamic pressure
What is a pitot-static tube used for?
Since Ps = Pinf + 1/2(rho)(Uinf^2)
By measuring both the stagnation and static pressure, the instrument allows for the velocity of fluid flow to be measured
What is a syphon?
A syphon is a tube in an inverted U shape which causes a liquid to flow uphill, above the surface of the reservoir, without pumps, before discharging at a low elevation
The fluid is able to flow uphill because it knows about the lower level on the other side through pressure
What is a venturi tube?
A device for determining the volume flux Q (or equivalently U) in a pipe
