1. The flow between points P1 and P2 is steady, non-uniform flow since the water depth changes along the length of the ditch but the discharge is constant. 2. Comparing the total head at P1 and P2 using Bernoulli's equation with an energy loss term shows that there is a 0.3 m energy loss between the two points over a 1500 m length of ditch. 3. The flow is classified as one-dimensional flow since the width and depth of flow are much smaller than the length between P1 and P2.

1. 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]

2. Bernoulli’s law (without energy losses)
2 2
u u
y1  z1  y2  z2  2
 y 3  z3 3
 constant
2g 2g

6. 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]

7. 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.

8. 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
3 example; channel with different A and Q

9. 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

12. Bernoulli’s law, with head loss
2 2
u u
y1  z1  1
 y 2  z2   H12
2
2g 2g
Head loss [m]
u12/2g ΔH
Total Head H [m]
y1 u22/2g Velocity Head [m]
P1
u1 Surfacelevel y +z [m]
z1 y2
P2
u2>u1 z2
6 Reference [m]

16. 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]

17. 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.