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 [m] 2g

uξΔΗ

2

culvertculvertculvert

21

2

222

2

111

22 H

g

uzy

g

uzy

P1 P2

Friction loss, Darcy Weisbach

R

Lf

4

2

Inlet and outlet loss [intree en uitree verlies]

2

11

i

1o

µ=contraction coëfficiënt (bv 0,6) [1]

2

Outlet los

3,0u 5,0u

2

Loss at a (open) valve [klep]

Loss at a non-return valve

[terugslag klep]

0,2 and 0,1 Between

1 elyapproximat

2

Head (energy) loss strategy

[m] 2g

uξΔΗ

2

[m] 2g

u)ξξξ(ΔΗ

2

.....21total

[m]2g

uξ

2g

uξ

2g

uξΔΗ

2

.......

2

22

2

11total

If velocity does not change

2

Head (energy) loss culvert

2

11

i

1oR

Lf

4

[m] 2g

u)ξξξ(ΔΗ

2

culvertoficulvert 2

Submerged Culvert 1 [Volledig gevuld]

2g

uξΔΗ

2

ctottot

....)ξξξ( ofi tot

2

11

i

R

lf

4

1o

∆𝐻𝑡𝑜𝑡 = Total Head Loss Culvert [m]

𝜉𝑡𝑜𝑡 = Sum of Loss coefficients [1]

𝑢𝑐 = Mean Fluid Velocity Culvert [m/s]

𝜉𝑖 = Loss coefficient due to contraction [1]

𝜉𝑤 = Loss coefficient due to friction [1]

𝜉𝑜 = Loss coefficient due to outlet [1]

𝜇 = Contraction coefficient [1]

𝑔 = earths gravity [m/s2]

𝜆 = Friction coefficient [1]

R = Hydraulic Radius [m]

𝑙 = Length between the Head Loss [m] 2

Submerged Culvert 2

totcHgAmq 2

tot

m

1

2b

2g

uξΔΗ

2

ctottot

𝑄 = 𝑢 ∙ 𝐴

Submerged Culvert 2

totcHgAmq 2

tot

m

1

q = Flow rate Culvert [m3/s]

𝑚 = Discharge coefficient [m]

𝐴 = Wetted Area Culvert [m2]

∆𝐻𝑡𝑜𝑡 = Total Head Loss Culvert [m]

𝜉𝑡𝑜𝑡 = Sum of Loss coefficients [1]

𝑔 = earths gravity [m/s2]

2b

Culvert, no upstream and downstream

velocity

3

∆y=∆H

Difference in water level = Difference in total head

Culvert, with upstream and downstream

velocity

3

∆y≠∆H

Difference in water level ≠ Difference in total head

Culvert, with upstream and downstream

velocity

3

21

2

222

2

111

22 H

g

uzy

g

uzy

[m] 2g

uξΔΗ

2

culvertculvertculvert

P1 P2

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