Energy conservation Part 1

Question 1

Where is the steady Bernoulli equation derived from?

Answer 1

This equation is derived from the principle of conservation of energy, where the sum of kinetic energy, potential energy, and fluid pressure remains constant along a streamline in a steady, inviscid flow.

Question 2

How does total energy behave along a streamline?

Answer 2

Constant

Question 3

What is Bernoulli equation?

Answer 3

E = P + ρgz + 1/2ρU^2

Question 4

True or false, pressure and velocity are directly related?

Answer 4

True

Question 5

What are the assumptions made?

Answer 5

• Steady flow
• Constant density
• Dissipation-less flow

Question 6

What is the Bernoulli equation in terms of head?

Answer 6

H = P/ρg + z + U^2/2g

Question 7

What are the units of the head equation and all the terms in the head equation?

Answer 7

m

Question 8

What does the pressure head represent?

Answer 8

Represents the column of fluid required to produce the pressure 𝒑

Question 9

What is the piezometric head?

Answer 9

h = P/ρg + z

Question 10

How does the piezometric head behave in the vertical when pressure is hydrostatic?

Answer 10

Constant

Question 11

How can pressure be calculated?

Answer 11

P = ρg(h-z)

Question 12

When is flow static?

Answer 12

When U=0 and H=h

Question 13

What are the energy and hydraulic grade lines?

Answer 13

Graphical representation of the energy state of the fluid

Question 14

What is the difference between the energy grade line and hydraulic grade line?

Answer 14

The velocity head

Question 15

What is the continuity equation for volume flux?

Answer 15

A1U1=A2U2

Question 16

How does Q, discharge behave horizontally?

Answer 16

Q discharge is constant on a horizontal streamline with points at the same elevation.

Question 17

What happens as velocity increases?

Answer 17

Pressure decreases

Question 18

If a vortex is created what is the pressure distribution?

Answer 18

Low pressure at the centre of the circle and high pressure on the outside

Question 19

What does it mean if there is a stronger curvature in the vortex?

Answer 19

R is smaller and there is a larger ∆P

Question 20

How does piezometric head behave along a streamline?

Answer 20

It is the same along it

Question 21

What does the second Bernoulli equation provide information about?

Answer 21

The pressure inside a fluid body

Question 22

When is Bernoulli valid?

Answer 22

• Converging streamlines
• Accelerating fluid
• Low energy losses

Question 23

When is Bernoulli not valid?

Answer 23

• Diverging streamlines
• Decelerating fluid
• Turbulence - energy losses

Question 24

How can you slow down a fluid?

Answer 24

In order to slow fluid down the pressure must increase and the flow separates

Question 25

In a draining reservoir at what pressure does the flow exit?

Answer 25

Atmospheric pressure

Question 26

What is a Vena Contracta?

Answer 26

Streamlines there are locally straight and parallel -> where the diameter is the least

Question 27

In a draining resevoir how does velocity depend on distance to the free surface?

Answer 27

U = √2gh_s

Question 28

What is the pressure at the stagnation point along the same streamline?

Answer 28

P_s = P1 + 1/2⍴U^2

Question 29

What does it mean when there is a stagnation point in the mouth of the tube?

Answer 29

No flow out of or into the tube

Question 30

How do you force flow along a pipe?

Answer 30

Apply a greater pressure

Question 31

What is a syphon?

Answer 31

A syphon is a tube in an inverted U shape that causes a liquid to flow uphill

Question 32

How does a syphon work?

Answer 32

• Doesn’t need a pump and discharging at low elevations
• The fluid is able to flow uphill because it knows about the lower level on the other side through pressure

Question 33

What is the static pressure?

Answer 33

P_∞

Question 34

What is the dynamic pressure?

Answer 34

1/2⍴U^_∞

Question 35

What is the stagnation pressure?

Answer 35

P_s