Traffic and Highway Engineering
Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Chapter 16, Problem 19P
To determine

Whether the given culvert will operate under inlet or outlet control for the given conditions.

Expert Solution & Answer
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Answer to Problem 19P

The given culvert is acceptable and the inlet control governs.

Explanation of Solution

Given:

The dimension of concrete box is 5ft×5ft.

The angle of inclination of flared walls is 45°.

The 50 years flow rate is 200ft3/sec.

The design headwater elevation is 105ft.

Elevation of stream bed at face of invert is 99.55ft

Tail water depth is 4.75ft

Approximate length of culvert is 200ft

Slope of stream is 1.5%.

The value of n is 0.012.

The value of k is 0.5.

Formula used:

The flow rate per width is given by,

  q=QB ....... (I)

Here, Q is the discharge and B is the width.

The required headwater is given by,

  HWi=(HWD)(depthofculvert) ....... (II)

Here, HWD is the headwater depth at culvert face.

The design headwater depth is given by,

  HWd=ELhdELsd ....... (III)

Here, ELhd is the design headwater elevation and ELsf is the elevation at the stream bed at the face.

The formula for fall is given by,

  Fall=HWiHWd ....... (IV)

The culvert invert elevation is given by,

  Culvert invert elevation=ELsfFall ...... (V)

The depth from outlet invert to hydraulic line is given by,

  ho=(dc+d)2 ...... (VI)

Here, dc is the critical depth and D is the depth of box.

The outlet water elevation is given by,

  ELo=(Culvert invert elevationS0)(Approximatelengthofculvert) ...... (VII)

Here, S0 is the slope.

The required outlet headwater elevation is given by,

  ELho=ELo+H+ho ...... (VII)

Here, H is the total head loss.

Calculation:

The flow rate per width is calculated as,

Substitute 200ft3/sec for Q and 5ft for B in equation (I).

  q=200ft3/sec5ft=40ft2/sec

Consider Figure 16.16, "Headwater Depth for Inlet Control, Rectangular Box Culverts, Flared Wingwalls 18° to 33.7° and 45° with Beveled Edge at Top of Inlet" from the book "Traffic and Highway Engineering", for a height of 5ft and flow rate per width of 40CFS/ft, the headwater depth of the culvert face HWD, is 1.19.

The required headwater is calculated as,

Substitute 1.19 for HWD and 5ft for depth of culvert in equation (II).

  HWi=1.19(5ft)=5.95ft

The design headwater depth is calculated as,

Substitute 105ft for ELhd and 99.55ft for ELsf in equation (III).

  HWd=105ft99.55ft=5.45ft

The fall is calculated as,

Substitute 5.45ft for HWd and 5.95ft for HWi in equation (IV).

  Fall=5.95ft5.45ft=0.50ft

The culvert invert elevation is calculated as,

Substitute 99.55ft for ELsf and 0.50ft for HWd in equation (V).

  Culvert invert elevation=99.55ft0.50ft=99.05ft

The depth from outlet invert to hydraulic line is calculated as,

Substitute 3.7ft for dc and 5ft for D in equation (VI).

  ho=(3.7ft+5ft)2=4.35ft

The tail water is greater so take ho=4.75ft.

The outlet water elevation is calculated as,

Substitute 99.05ft for culvert invert elevation, 0.015 for S0 and 200ft for approximate length of culvert in equation (VII).

  ELo=[99.05ft(0.015)(200ft)]=96.05ft

For n=0.012 the total head loss is 2.2ft.

The required outlet headwater elevation is calculated as,

Substitute 96.05ft for ELo, 4.75ft for ho and 2.2ft for H in equation (VIII).

  ELho=96.05ft+2.2ft+4.75ft=103ft ...... (VII)

The required outlet headwater elevation is less than the design headwater design so the given culvert is acceptable and inlet control governs.

Conclusion:

Therefore, the given culvert is acceptable and the inlet control governs.

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