cu06997 lecture 4_answer

Exercise 1

For the frictionless

syphon in Figure 2.4 (So

there is no energy loss),

determine the discharge

and the pressure heads at

A and B, given that the

pipe diameter is 200 mm

and the nozzle exit is

150 mm

Assume fresh water and

g = 10 [m/s2]

Bernoulli’s law (without energy losses)

constant22

2

333

2

22211

g

uzy

g

uzyzy

Exercise 2 Distance between P1 en P2 (L) = 1500 m

The ditch has a bed-slope [helling bodem] of 1:2000

Assume bed-slope = slope pressure line = slope total head

Water-depth (D) = 1,5 m at P1 and P2

Discharge Q = 21 m3/s

Bed width ditch (W) = 4 m

Slope ditch (S) = 1:3

Assume fresh water and g = 10 [m/s2]

Exercise 2

Questions:

1.Classify the flow at the part P1 – P2 (steady, unsteady, uniform, non

uniform)

2.Classify the flow at the weir (steady, unsteady, uniform, non uniform)

3.Is the flow between P1 – P2 one, two or three dimensional?

4.Is the flow at the weir one, two or three dimensional?

5.Compare P1 and P2 with Bernoulli’s equation (with energy loss)

6.Based on question 5, how much is the energy loss between P1 and P2.

Classification of flows

1. Steady uniform flow [Eenparig uniform] example: pipe with constant D and Q

example: channel with constant A and Q

2. Steady non-uniform flow example: pipe with different D and constant Q

example: channel with different A and constant Q

3. Unsteady uniform flow[Niet eenparig , uni..] example: pipe with constant D and different Q

example: channel with constant A and different Q

4. Unsteady non-uniform flow example: pipe with different D and Q

example; channel with different A and Q 3

Visualization of flow patterns

A streamline [stroomlijn] is a

line representing the direction

of flow. Streamlines can not

cross

A set of streamlines may

be arranged to form a

imaginary pipe. This is

called a streamtube

[stroombaan]

4

Bernoulli’s law, with head loss

u1

Reference [m]

Surfacelevel y +z [m]

Total Head H [m]

P1

z1

y1

u12/2g

P2 z2

y2

u22/2g

u2>u1

21

2

222

2

111

22 H

g

uzy

g

uzy

Head loss [m] ΔH

Velocity Head [m]

6

Exercise 3 Distance between P1 en P2 (L) = 1500 m

The bed of the ditch is horizontal

Water-depth (D) = 1,5 m at P1

Water-depth (D) = 1,2 m at P2

Discharge Q = 21 m3/s

Bed width ditch (W) = 4 m

Slope ditch (S) = 1:3

Assume fresh water and g = 10 [m/s2]

Exercise 3

Questions:

1.Classify the flow at the part P1 – P2 (steady, unsteady, uniform, non

uniform)

2.Classify the flow at the weir (steady, unsteady, uniform, non uniform)

3.Is the flow between P1 – P2 one, two or three dimensional?

4.Is the flow at the weir one, two or three dimensional?

5.Compare P1 and P2 with Bernoulli’s equation (with energy loss)

6.Based on question 5, how much is the energy loss between P1 and P2.