Two different types of pressure ??
Two different types of pressure ??
(OP)
Imagine a pipe whose diameter changes (pipe reduction or pipe expansion)
Let's define two different places in that pipe:
point 1: with a pressure P1, velocity V1 and diameter D1;
and point 2: with a pressure of P2, velocity V2 and and D2.
Knowing that the fluid flows from point 1 to point 2, the pipe is horizontal (no level change) and D2 > D1: applying a material balance we know that V2 < V1 then applying an energy balance (i.e. Benouilli's equation) we know that P2 > P1 (pressure drop in the pipe has been considered very low and irrelevant). Therefore the fluid is flowing from a low pressure place (point 1) to a high pressure place (point 2) !!! How can that be ?
Let's define two different places in that pipe:
point 1: with a pressure P1, velocity V1 and diameter D1;
and point 2: with a pressure of P2, velocity V2 and and D2.
Knowing that the fluid flows from point 1 to point 2, the pipe is horizontal (no level change) and D2 > D1: applying a material balance we know that V2 < V1 then applying an energy balance (i.e. Benouilli's equation) we know that P2 > P1 (pressure drop in the pipe has been considered very low and irrelevant). Therefore the fluid is flowing from a low pressure place (point 1) to a high pressure place (point 2) !!! How can that be ?





RE: Two different types of pressure ??
That's what Bernoulli's principle is about.
If you take a pipeline vertically down to 100 meters and close it by a valve, the pressure gauge before the valve reads 10kg/sq.cm g. If the top end is open to atmosphere, the pressure there is 1kg/sq.cm (approx.). Open the valve and still you get the flow because total pressure at the high point is high. The closed valve maintains equal total pressure both sides and that is why you don't get flow.
Regards,
RE: Two different types of pressure ??
You need to look at the dynamic forces. The total force at 1 in the direction of flow is greater than the total force at 2 in the opposite direction and hence flow is from 1 to 2. The force is a combination of pressure and momentum and momentum is proportional to V^2.
In the same way the roller coaster rides uphill to the next crest.
RE: Two different types of pressure ??
You need to look at the dynamic forces. The total force at 1 in the direction of flow is greater than the total force at 2 in the opposite direction and hence flow is from 1 to 2. The force is a combination of pressure and momentum and momentum is proportional to V^2.
In the same way the roller coaster rides uphill to the next crest.
RE: Two different types of pressure ??
To bct1981.
Fluids move from high mechanical energy points to points of lower mechanical energy. Pressure is just one component of mechanical energy.
The total mechanical energy in a point per unit mass is the sum of
p/ρ the work on the fluid by displacing
it through a volumetric space 1/ρ gainst the
restraint of pressure p,
V2/2 the kinetic energy per unit mass,
zg the potential energy per unit mass with
the horizontal reference level 0-0
If you multiply these summands by mass you get energy units.
Neglecting friction, as Bernoulli did for incompressible fluids, the mechanical energy balance between points 1 and 2 shows:
Dividing them by g (acceleration of gravity) they become expressed in lengths, for example, m or ft.
Static head difference: (P2-P1)/ρg
Velocity head difference: ΔV2/2g
Elevation difference: Δz
Real fluids convert some of their mechanical energy into heat due to friction. This loss of mechanical energy can be expressed as a loss in static head (or pressure), and can be expressed as ΔPf/ρg
RE: Two different types of pressure ??
The answer is not in reinstating Bernoulli equation but in analysis of fluid dynamics and the balance of forces. (Momentum balance) .
The upstream force = the downstream force – the friction loss.
Force = pressure over area + momentum.
Momentum = V x Q. gamma/g
and since Q=VA
Momentum is proportional to V^2
The friction loss is also proportional to V^n.
What nature is able to do is to solve these iterative equations and create a balance.
RE: Two different types of pressure ??
To BRIS, don't forget elevation (potential energy). See quark's example.
Eppur si muove...It is clear from the energy balance equation that for a fluid to move from point 1 to point 2, it needs its energy to be larger at point 1.
This can be achieved, even when P1<P2, only when the other energy components compensate to make energy1 > energy2.
RE: Two different types of pressure ??
The question is
Therefore the fluid is flowing from a low pressure place (point 1) to a high pressure place (point 2) !!! How can that be ?
The anser is
Because the water has greater momentum at point 1 than point 2. The force at point 1 is greater than the force at point 2 so the fluid moves from point 1 to point 2. QED.
RE: Two different types of pressure ??
You are right, BRIS, in admitting that momentum (p=m×v) alone could not explain the draining of a vertical tank.
In fluid dynamics Bernoulli's equation expresses the conservation of energy; however one needs also conservation of mass (the continuity equation v1A1=v2A2) to explain a horizontal Venturi flowmeter. (v: velocity; A: crossflow area)
The dirt around a prairie dog's hole is mounded up in a way that forces wind to accelerate over the hole, resulting in lower pressure above the hole. Biologists speculate this design has evolved to provide natural ventilation.
One can suspend a ping-pong ball inside an inverted funnel by blowing air downward through it. Rapid divergence of the flow results in lower speed and therefore higher pressure below the ball.
All these effects and many more such as lift in flight, spinning balls curved trajectories, wind turbines, etc., can be explained by Bernoulli's formula.
RE: Two different types of pressure ??
RE: Two different types of pressure ??
BRIS, since mechanical force is the rate change of momentum (Newton's second law of motion), this force could be used to interpret motion of matter including flow in rotational fields.
Philosophically speaking about the variety of forces, you are absolutely right.
BTW, another universal law is the conservation of linear momentum. Bernoulli's law however, is quite general, and serves to explain a wide variety of effects.
There are indeed many forces in Nature besides gravity that act by affecting motion of matter in general, and liquids, in particular.
Common among them are chemical potential changes due to concentration gradients as in osmosis, or capillarity from adhesion and cohesion forces, etc.
Not to mention electromagnetic and other yet unknown forces (called colors) acting in the subatomic realm and on stars.
Would a grand unification theory (GUT) in the future merge all these forces as a manifestation of a single common interaction ? Who knows.
RE: Two different types of pressure ??
Is static head the result of elevation differences? With static pressure being the pressure difference at the two selected points of observation.
RE: Two different types of pressure ??
"the sum of the static pressure, velocity pressure and static head" are the variables in Bernoulli’s equation
RE: Two different types of pressure ??
Macmet,
By static head, I mean the elevation and static pressure is what we generally call as pressure.