Pipe systems and energy losses

Question 1

How does the Bernoulli equation work for pipe flow?

Answer 1

• An equation that works over the whole cross-section of the pipe
• Assume streamlines are approximately parallel
• Account for wall friction and other losses

Question 2

What is the Bernoulli equation for the entire cross-section of a pipe?

Answer 2

H = h + ⍺U^2/2g
- U is the velocity averaged over the cross-section

Question 3

What is the value of alpha for a uniform profile across a pipe?

Answer 3

1

Question 4

What is the value of alpha for a turbulent profile in a pipe?

Answer 4

⍺ ≈ 1.06

Question 5

What is a major loss?

Answer 5

Losses due to friction with the wall

Question 6

What is a minor loss?

Answer 6

• Losses due to pipe bends, contractions, entries, exits, fittings and valves
• Minor losses can often dominate over major losses

Question 7

How can minor an major losses be incorporated in energy balance?

Answer 7

Both major and minor losses can be incorporated by adding a head loss term to the Bernoulli equation

Question 8

What value does the loss value usually have?

Answer 8

Between 0 and 1

Question 9

What do big constrictions mean?

Answer 9

Higher loss factor

Question 10

What is the entrance loss denoted by?

Answer 10

𝜉U^2/2g

Question 11

What does a sudden expansion mean in terms of energy?

Answer 11

Large energy loss

Question 12

What is the exit loss denoted by?

Answer 12

U^2/2g

Question 13

Why is the exit loss the same as the velocity head?

Answer 13

All KE lost if a pipe discharges into a reservoir -> assume all KE in flow has been dissipated

Question 14

What does the height in the pitot tube suggest?

Answer 14

The height in the pitot tubes suggests the height of the EGL

Question 15

How can you caluclate the enrgy loss?

Answer 15

∆H_L = ∆H_x+∆H_e

Question 16

How can you determine the pressure grade line?

Answer 16

hydraulic grade line - z

Question 17

How does the flow rate change between two reservoirs in a pipe?

Answer 17

The volume flow rate is free to flow

Question 18

Why might the hydraulic grade line dip between two reservoirs?

Answer 18

Flow accelerates so pressure decreases

Question 19

When do the grade lines coincide?

Answer 19

At the free surface

Question 20

What will happen to the velocity as a result of local energy losses?

Answer 20

Smaller flow velcoities

Question 21

What is pipe skin friciton?

Answer 21

Energy is lost due to friction on the walls.

Question 22

What is the formula for skin friction?

Answer 22

∆H_f = fL/DU^2/2g

Question 23

What is f in the skin friciton equation?

Answer 23

f is the (dimensionless) Darcy-Weisbach friction coefficient.

Question 24

When is the skin friction equation valid?

Answer 24

For ciruclar pipes only

Question 25

Becuase of skin friciton how will the energy grade line be drawn?

Answer 25

Energy grade line is a downward slope with distance along the pipe

Question 26

What does the frcition coefficient depend?

Answer 26

Depends on roughness and on the Reynolds number

Question 27

When does f become constant?

Answer 27

Rough walls with high Re

Question 28

Whats the difference between velocity heads in pipes with different diameters?

Answer 28

Velocity head in larger pipe is smaller than the smaller pipe

Question 29

How will rate of fricitonal loss differ in pipes with different diameters?

Answer 29

Rate of frictional loss will be less in large pipes as the diameter is larger

Question 30

What is the equation for major head loss for noncircular pipes?

Answer 30

∆H_f = fL/D_eU^2/2g

Question 31

What is the diameter equivalent

Answer 31

It is the diameter of a circular duct or pipe that gives the same pressure loss as an equivalent rectangular duct or pipe for a particular flow rate.

Question 32

How do you find the hyraulic diameter?

Answer 32

4A/P