CL420 Water Engineering 2

CL420 Water Engineering 2GVF in an open channel (H41)

IntroductionWhen the weight component of a fluid is equal to the friction caused by the bed and sides then uniform flow is present. This is only likely to occur in artificial channels. This can be seen in Figure 1. Gradually Varied Flow (GVF) is where the flow accelerates or decelerates over a period of time. This happens when there is a net force acting on the flow. This can be seen in Figure 2. It shows that if weight + pressure > friction then the flow will accelerate and if friction + pressure > weight then the flow will decelerate.

GVF happens between do (uniform flow) and dc (critical flow) and is a gradual move away from do towards dc. This is caused by a change in geometry of the channel but the bed slope and friction are also important factors.

TheoryFlow Classification There is 12 categories in which flow profiles can be put in. These categories depend on the slope and also the depth of flow relative to do and dc. These can be seen in Figure 3.

Critical depth The critical depth occurs when the Froude number, Fr=u/(gD)1/2 =1 where D is the hydraulic depth, D=A/T where A=cross sectional area of the flow and T=top width. For a rectangular cross section then T=B and A=Bd so D=d where B is the channel width and d is the water depth so, Fr=u/(gd)1/2=1 and therefore u=(gd)1/2 , where g is the acceleration due to gravity and d is the water depth. This depth is known as the critical depth (dc) so, dc=u/g. In terms of discharge, Q=Au=(Bdu) m3 s-1, where B is the width of the rectangular channel so, dc=(Q2/gB2)1/3 or in terms of discharge per unit width q m2 s-1, dc=(q2/g)1/3. The critical depth is independent of bed slope and of the bed roughness. For a given channel, dc depends only on discharge q. Normal depth Normal depth (do) occurs when s=i=nu/R4/3, where s=bed slope, i=friction slope (weight component down-slope equals friction force up-slope). The flow must also be uniform for normal depth. In terms of discharge Q=Au therefore, Q=AR2/3s1/2/n (m3 s-1) which is the Manning equation. Where n is the Manning friction coefficient and the hydraulic radius R=A/P cross section area. For a rectangular channel this gives, R=Bd/(B+2d)=d/[1+(2d/B)],

The normal depth depends on q=Q/B and also the channel geometry. The equation gives do in terms of do and therefore the value is approximated through a series of iterations.Critical Slope

EquipmentAn Armfield tilting flume with two trolley mounted vernier probes will be used to take measurements of depth along the flume. Method1) Set s=0.000 and put stop log in. Measured the depth of the pool and the bed level. The width of the channel was taken at the chainage points.2) Measured the flow rate, Q m3 s-1. 3 measurements were taken of the time to fill the reservoir and the average was taken. This was then used to in the equation Q=V/t. 3) Calculate do and dc by hand calculation for s=0.002 and s=0.0125. 4) Set s=0.0125 and take measurements at chainage points. Mean depth ~ 26mm then n=0.0076 m-1/3 s and is an acceptable value for the calculations.5) Evaluate the critical slope and show how to check if a slope is steep or mild. 6) Set s=-0.0025 and insert a sluice gate at 4m chainage. Measure and sketch the profile A3+HJ+H2. 7) Keeping sluice gate in same position and set s=0.000. Measure and sketch the profile H3+HJ+H2. 8) Keeping sluice gate in same position and set s=0.002. Measure and plot the profile M3. 9) Remove sluice gate and set s=0.000. Measure and plot the profile H2. Find dc and evaluate the Froude number at each chainage. 10) Set s=0.002. Measure and plot the profile M2. 11) Set s=0.0125 and insert a 50mm stop log at end of flume to create an exit weir. Measure and plot the profile S1.Measurements

See Appendix A for all measurements taken

GVF Profiles

S1

M2

Discussion

Conclusions

Appendix A

Horizontal (No Flow)

Steep?????? S=0.0125

A3+HJ+A2

H3+HJ+H2

M3

H2

M2

S1