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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)

                    2              2
                    u               u
y1  z1  y2  z2  2
                        y 3  z3 3
                                        constant
                    2g              2g
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
3     example; channel with different A and Q
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
                    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]
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.
Cu06997 lecture 4_answer
Cu06997 lecture 4_answer
Cu06997 lecture 4_answer

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Cu06997 lecture 4_answer

  • 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
  • 3.
  • 4.
  • 5.
  • 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
  • 10.
  • 11.
  • 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]
  • 13.
  • 14.
  • 15.
  • 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.