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Design of Roadside Channels with Flexible Linings
Hydraulic Engineering Circular Number 15, Third Edition

Appendix B: Channel Geometry Equations

definition sketch for v shape channel. A equals B times d plus Z times d squared, P equals B plus  2 times d times square root of (Z squared plus 1), T equals B plus 2 times d times Z

definition sketch for trapezoidal channel. A equals B times d plus Z times d squared, P equals B plus 2 times d times square root of (Z squared plus 1), T equals B plus 2 times d times Z

definition sketch for a parabolic channel. A equals two-thirds T times d, P equals one-half times square root of (16 times d squared plus T squared) plus T squared divided by 8 divided by d times natural logarithm of ((4 times d plus square root of (16 times d squared plus T squared)) divided by T), T equals 1.5 times A divided by d

definition sketch for v-shape with rounded bottom channel as defined below

2 CASES

No. 1

If d ≤ 1/Z, then:

A equals eight-thirds times d times square root (d times Z)
P equals 2 times Z times the natural logarithm of (square root of (d divided by Z) plus square root of (1 + d divided by Z)) plus 2 times square root of (d squared plus d times Z)
T equals 4 times the square root of (d times Z)

No. 2

If d > 1/Z, then:

A equals eight-thirds times d plus 4 times (d minus 1 over Z) plus Z times (d minus 1 over Z) squared
P equals 2 times Z times the natural logarithm of (1 plus the square root of (Z squared +1) divided by Z) plus 2 times square root of (Z squared plus 1) divided by Z plus 2 times (d minus 1 over Z) times square root of (1 + Z squared)
T equals 4 plus 2 times Z times (d minus 1 over Z)

Note: The equations for V-shape with rounded bottom only apply in customary units for a channel with a 4 ft wide rounded bottom.

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Updated: 04/07/2011
 

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