Q.No. 02 Verify by computation the depth velocity relationships shown in figure below for the four flow regimes in a wide rectangular open channel. The 





temperature of the water is taken as 68^{°}F. Depth Vs Velocity Chart 










Figure 1 










SOLUTION: 





For verification of type of depth velocity relationship first we will assume a wide 


rectangular channel with a constant width then we will take values of V and Y from 


the given figure and by calculations we will verify our assumptions 









Channel width 
= 
2 
ft 


Flow range & type 
= 
Subcritical Laminar 1 


Flow Velocity 
= 
0.2 
ft/s 


Flow depth 
= 
0.02 
ft 


Acc gravity 
= 
32.2 
ft/s 








Hydraulic radius 
= 
0.0196 



υ 

= 
0.0000108 
ft2/s 
@ 68F 
Froud No 
= 
0.25 



Rynold's No 
= 
364 



For Froud's No 0.25 and Rynold's No 364 it can be verified from Figure.1, that Flow is in Subcritical Laminar 1 





Channel width 
= 
2 
ft 

Flow range & type 
= 
Supercritical Laminar 2 

Flow Velocity 
= 
2 
ft/s 

Flow depth 
= 
0.0025 
ft 

Acc gravity 
= 
32.2 
ft/s 






Hydraulic radius 
= 
0.0025 
ft 

υ 

= 
0.0000108 
ft2/s 
Froud No 
= 
7.05 


Rynold's No 
= 
462 


For Froud' No 7.05 and Rynold's No 462 it can be verified from Figure.1, that Flow is in Supercritical Laminar 2 









Channel width 
= 
2 
ft 

Flow range & type 
= 
Supercritical Turbulent 3 

Flow Velocity 
= 
10 
ft/s 

Flow depth 
= 
0.1 
ft 

Acc gravity 
= 
32.2 
ft/s 






Hydraulic radius 
= 
0.0909 
ft 

υ 

= 
0.0000108 
ft2/s 
Froud No 
= 
5.57 


Rynold's No 
= 
84176 


For Froud's No5.57 and Rynold's No 84176 it can be verified from Figure.1, that Flow is in Supercritical Turbulent 3 




Channel width 
= 
2 
ft 

Flow range & type 
= 
Subcritical Turbulent 4 

Flow Velocity 
= 
0.25 
ft/s 

Flow depth 
= 
0.1 
ft 

Acc gravity 
= 
32.2 
ft/s 






Hydraulic radius 
= 
0.0909 
ft 

υ 

= 
0.0000108 
ft2/s 
Froud No 
= 
0.14 


Reynold's No 
= 
2105 


For Froud's No 0.14 and Rynold's No 2105 it can be verified from Figure.1, that Flow is in Subcritical Turbulent 4 




Also See: Factors Affecting Water Hammer