Fluid Mech Sem 2 Flashcards
State Bernoulliโs equation
1/๐๐๐ฝยฒ+๐+๐๐z = constant along a streamline
What is a streamline?
A line used to represent particle paths in a steady flow
What is fundamental about streamlines in an inviscid flow?
Energy is conserved along them
What are the 3 energies included in Benoulliโs equation?
Kinetic energy
Potential energy
Pressure โenergyโ
What term in the Bernoulli equation can often be neglected?
The potential energy, ๐๐z in AIR BUT NOT IN WATER
In air, for the height change to be big enough youโve probably moved far enough so the density of air has also changed
But in water the pressure changed add up much more quickly so cannot be neglected
What is Head, H?
The height to which the water could be pumped if all the pressure and kinetic energy were converted to potential energy
Write the Bernoulli equation in terms of head (divide by ๐๐)
H = ๐/๐๐+๐ยฒ/2๐+๐ง
What does Bernoulliโs equation NOT model?
The losses eg due to friction in pipes (so the Head will be lower than suggested)
What is stagnation pressure?
The pressure available if you stagnate the flow
What is the dynamic pressure?
The pressure available in kinetic energy
What is the equation to find stagnation pressure?
pโ+ 1/2 ๐(๐โ)ยฒ = pโ
pโ is static pressure - measured pressure
When can you use bernoulli?
Bernoulliโs equation can only be used in situations where you can draw a
streamline, and where there is no loss. This means that Bernoulliโs equation
cannot be applied to unsteady flows, mixing, flows with non-negligible
viscosity etc.
What is the equation to find dynamic pressure
1/2 ๐(๐โ)ยฒ = pโ - pโ
Pressure from kinetic energy
When can air be considered incompressible -> can use Bernoulli?
Below speed of 85 - 100m/s
(below Mach 0.25 - 0.3)
How does a pitot-static stube measure the velocity of a flow?
Via the dynamic pressure, which is the difference between the stagnation and static pressure
