CU06997 Fluid Dynamics
Flow in pipes and closed conduits
4.5 Turbulent flow (page 100-111)
4.6 Local head losses (page 112-116)
4.7 Partially full pipes (page 116-121)
1

Culvert, no upstream and downstream
velocity
1

Culvert, with upstream and downstream
velocity
1

Culvert, no upstream and downstream
velocity 2 2
u1 u2
y1  z1   y 2  z2   H12
2g 2g
P1 P2
2
u
2 ΔΗ culvert  ξ culvert  culvert
[m]
2g

Friction loss, Darcy Weisbach
L
f   
4R
2

Inlet and outlet loss [intree en uitree verlies]
o  1
2
1 
 i    1
 
 
µ=contraction coëfficiënt (bv 0,6) [1]
2

Outlet los
u  0,3 u  0,5
2

Loss at a (open) valve [klep]
  Between 0,1 and 0,2
Loss at a non-return valve
[terugslag klep]
  approximately 1
2

Head (energy) loss strategy
2
u
ΔΗ  ξ  [m]
2g
2 2 2
u u u
ΔΗ total  ξ1   ξ 2   ξ... 
1 2
[m] ....
2g 2g 2g
If velocity does not change
2
u
ΔΗ total  (ξ1  ξ 2  ξ..... )  [m]
2 2g

Head (energy) loss culvert
o  1
2
1  L
 i    1
  f   
  4R
2
u
ΔΗ culvert  (ξ i  ξ f  ξ o )  culvert
[m]
2 2g

Submerged Culvert 1 [Volledig gevuld]
u2 tot  (ξ i  ξ f  ξ o  ....)
ΔΗ tot  ξ tot  c
2g
∆𝐻 𝑡𝑜𝑡 = Total Head Loss Culvert [m] 1 
2
𝜉 𝑡𝑜𝑡 = Sum of Loss coefficients [1]  i    1
 
𝑢𝑐 = Mean Fluid Velocity Culvert [m/s]  
𝜉𝑖 = Loss coefficient due to contraction [1]
l
𝜉𝑤 = Loss coefficient due to friction [1] f   
4R
𝜉𝑜 = Loss coefficient due to outlet [1]
𝜇 = Contraction coefficient [1]
𝑔 = earths gravity [m/s2] o  1
𝜆 = Friction coefficient [1]
R = Hydraulic Radius [m]
𝑙 = Length between the Head Loss [m] 2

Submerged Culvert 2
2
u
ΔΗ tot  ξ tot  c
2g 𝑄= 𝑢∙ 𝐴
1
m
 tot
q  m  Ac  2 g  H tot
2b

Submerged Culvert 2
q  m  Ac  2 g  H tot
1
m
 tot
q = Flow rate Culvert [m3/s]
𝑚 = Discharge coefficient [m]
𝐴 = Wetted Area Culvert [m2]
∆𝐻 𝑡𝑜𝑡 = Total Head Loss Culvert [m]
𝜉 𝑡𝑜𝑡 = Sum of Loss coefficients [1]
𝑔 = earths gravity [m/s2]
2b

Culvert, no upstream and downstream
velocity
∆y=∆H
Difference in water level = Difference in total head
3

Culvert, with upstream and downstream
velocity
∆y≠∆H
Difference in water level ≠ Difference in total head
3

Culvert, with upstream and downstream
velocity
2 2
u u
y1  z1  1
 y 2  z2  2
 H12
2g 2g
P1 P2
2
u
ΔΗculvert  ξ culvert  culvert
[m]
3 2g

Exercise 1 culvert
•Difference in waterlevel 1 m
•Dimensions culvert 2 x 2 m
•μ=0,6 and λ = 0,022
•Calculate Q and draw the H and y line

Discharge culvert

Exercise 2 culvert
•Difference in waterlevel 1 m
•Dimensions culvert 2 x 2 m
•μ=0,6 and λ = 0,022
•u upstream = 0,5 m/s, u downstream = 0,2 m/s
•Calculate Q and draw the H and y line