CU06997 Exercise lecture 5 ; computation

Link to exercise lecture 5

Exercise 1 plus answer

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

Questions:

Calculate the Hydraulic Radius for the cross-section
A = 1.5 x (4 + 3*1.5) = 12.75 m2
P = 4 + 2 * (1.5² + 4.5²)^0.5= 13.5 m2
R=12.75/13.5=0.95 m
Calculate Reynolds number
u = Q/A = 21/12.75 = 1.65 m/s
ν = 10^-6 =kinematic viscosity
Re = 6270000 > 4000 so turbulent
Is the flow laminar or turbulent?
Re = 6270000 > 4000 so turbulent
From which velocity will the flow be laminar, assuming the cross-section stays the same.
Re should be less then so V<0.5 mm/s
From which velocity will the flow be turbulent, assuming the cross-section stays the same.
Re should be more them so V>1 mm/s

Exercise 2 plus answer

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

Questions:

Calculate the Hydraulic Radius for the cross-section at P2
A = 1.2 x (4 + 3*1.2) = 9.12 m2
P = 4 + 2 * (1.5² + 3.6²)^0.5= 11.6 m2
R=9.12/11.6=0.79 m
Calculate Reynolds number at P2
Is the flow laminar or turbulent?

Exercise 3 plus answer
Calculate the hydraulic radius for the following cross-sections:

bed width b [m]	water depth y [m]	slope [-]	A[m2]	P[m]	R[m]
4	1.45	1:3	12.11	13.17	0.92
3	1.37	1:2	7.86	9.13	0.86
5	2.98	1:4	50.42	29.57	1.71
400	3.2	1:0	1280	406.4	3.15

Exercise 4 plus answer
Calculate the hydraulic radius for the following partially filled pipes
I used the next table, calculate h/D look en table en find R/D

Cu06997 table pipe_block 5 from Henk Massink

Diameter D [m]	Water depth h [m]	h/d	table R/D	R [m]
0.8	0.7	0.875	0.3014	0.24
0.7	0.3	0.429	0.2243	0.16
3.4	1.7	0.5	0.25	0.85
2.8	2.0	0.714	0.2979	0.83

Slides

Cu06997 exercise5 from Henk Massink

CU06997 Exercise lecture 5 ; computation

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