What does the Bernoulli principle state?
Bernoulli’s Equation states that the work done on a fluid as it moves from one place to another is equal to the change in its mechanical energy.
βπ= βππΈ+ βπΎπΈ
(work energy relation)
When a liquid flowing through a pipe of two regions of different diameters, the velocity of the liquid will ____.
change.
The change in velocity involves an acceleration, a, which means there is a…
net force acting upon the liquid (F = ma).
π+1/2 ππ£^2+ππβ=ππππ π‘πππ‘
What does each represent?
Where P is the external pressure, 1/2 ππ£^2 is the kinetic energy and ππβ is the fluid pressure (potential energy).
Bernoulliβs Equation can only be used given the following assumptions:
- Fluid is incompressible (i.e. its density does not change).
- Fluid is non-viscous (i.e. no appreciable frictional effects).
- Fluid flow is streamline
. - Flow velocity at a fixed point does not change rapidly (i.e. steady state conditions apply).
i.e. Bernoulliβs Equation is only an approximation
If Velocity Increases –>
If Velocity Decreases –>
Pressure Decreases
Pressure Increases
P + πgh is the _______ term.
pressure
Β½ πv2 is the ______ term.
velocity
An aneurysm is a
swelling in a blood vessel which may rupture β can be fatal.
Aneurysms usually occur due to a…
weakness in the wall of the vessel which βbubblesβ due to the fluid pressure within the vessel.
Once an aneurysm starts, it will continue to grow until:
- It cannot grow anymore because of an obstruction (bone or tissue obstruction or stent),
- The elastic tension in the vessel wall is large enough to contain it,
- It bursts.
The fact that the aneurysm continues to grow is a direct consequence of the Continuity Principle and the Bernoulli Principle, why?
- Since the fluid pressure acts perpendicular to the surface, it will cause the vessel wall to swell in the region of weakness
- As the cross-sectional area gets bigger, the velocity decreases (Continuity Equation).
As the velocity decreases, the fluid pressure increases (Bernoulli Principle).
Detected aneurysms may be treated by clamping the blood vessel or using a…
stent.
A stent is a…
cylindrical βtubeβ which can be placed within the lumen of the blood vessel at the location of the aneurysm.
A stent will contain the blood (allowing it to flow through it), but stop…
the fluid pressure from acting directly on the vessel wall where the aneurism exists.
High blood velocity past the constriction causes low BP in left vertebral artery. A reverse (downward) blood flow can then result in…
Subclavian Steal Syndrome which in turn results in Transient Ischaemic Attack.
Vessels in circulatory system suffers one of two fates:
1- Aneurysm
2- Obstruction due to clot
The value of g is critical, and if the body is exposed to external accelerations, then the pressure…
in each of the arteries will change [by r(g +/- a)h if the acceleration is in the up or down direction] β this is directly analogous to Effective Weight.
One-way valves in blood vessels passing through muscle help in…
venous return.
One-way valves keep blood from…
flowing backwards.
Defective valves means…
pooling of blood in leg veins (Varicose )
The use of the Bernoulli Principle to draw a second fluid into the initial fluid is called…
entrainment.
As the main fluid flows from the wider tube into the constricted tube, its flow speed…
increases because the cross-sectional area has decreased (Continuity Principle). Consequently, the fluid pressure in the constricted region decreases.
If the vertical tube is connected to a reservoir of other fluid, then this will be βentrainedβ into the main fluid provided the…
pressure in the constricted region is lower than that in the fluid reservoir.
