Continuity And Bernoulis Equation

Question 1

Continuity

Answer 1

Principle of mass conservation in a fluid system. Asserts that mass cannot be created/ destroyed within a control volume or flow field. The mass flowing into a system must equal the mass flowing out. This ensures the mass is conserved as the fluid moves through a control volume.
A1U1= A2U2, ρAU= ρA2U2
For incompressible fluids, ρ1=ρ2.

Question 2

What does AU= A2U2 assume

Answer 2

We assume Q1=Q2, volume is conserved, no leakages. They are the volumetric flow rates at points 1 and 2.
Can also say U2= A1U1/ A2.

Question 3

Bernoulis equation

Answer 3

Flow along a pipe going uphill, considering kinetic energy, gravitational potential energy, work done.
Work done: W= FΔx(1)- FΔx(2)

Question 4

Bernoullis principle

Answer 4

For horizontal flow, an increase in velocity must be accompanied by a decrease in pressure.
Lifts is generated by a high velocity and low pressure at the top, and low velocity and high pressure at the bottom.
The principle describes the relationship between pressure, velocity and elevation. Provides insights into how fluid behaves in different sections of a streamline.

Question 5

Limitations of Bernoulli’s equation

Answer 5

-work done on a fluid increases it’s kinetic energy.
-determining the forces acting on a fluid particle, applying F= ma
- assumes flow is steady, laminar, velocity doesn’t vary with time.
- inviscid flow, shear forces are negligible.
- fluid behaves as if it incompressible, density can be assumed to be constant.

Question 6

Contunuiuty