Written by Chris Goodell, P.E., D. WRE | WEST Consultants
Copyright © RASModel.com. 2012. All rights reserved.
In HEC-RAS, it is a well known modeling technique to increase the coefficients of contraction and expansion in the vicinity of a bridge for steady flow modeling.
This is done to capture the energy loss resulting from increased flow contraction approaching the bridge, and increased flow expansion when leaving the bridge. This energy loss is not accounted for in the friction loss, so HEC has added in the ability to account for it using the contraction and expansion coefficients, multiplied by the difference in velocity head between two cross sections. Typically, RAS modelers will apply the higher coefficients (0.3 for contraction, 0.5 for expansion) at Cross Sections 4, 3, and 2 of the traditional cross section layout for bridges (see figure at the bottom of this post). Cross Section number 1 (the most downstream of the 4-cross section layout) is typically left at the default values of 0.1 and 0.3, respectively.
A common question is “why is Cross Section #1 left with the default values?”
The coefficients of contraction and expansion are applied to the reach from the cross section at which they are defined to the next cross section downstream. In the energy equation,
, he represents the head loss from one cross section to the next. The equation for head loss, he, is:
Where C is the coefficient of contraction or expansion. Subscripts 1 and 2 represent the two neighboring cross sections. So here you can see clearly that the coefficient of contraction or expansion is applied over a reach, defined by L, which is the length between Cross Sections 1 and 2.
So, for bridge modeling, the reach from Cross Section 4 to 3 defines the zone of contraction as flow approaches the bridge. The higher coefficients are applied to Cross Section 4 in this case.
The reach from Cross Section 3 to 2 defines the fully contracted zone though the bridge. You could make a case that since the flow is fully contracted in this zone, that the typical coefficients should be used (0.1 and 0.3). However, since there is usually a higher amount of turbulence in this zone, traditionally everyone keeps the higher coefficients (0.3 and 0.5). The higher coefficients are applied to Cross Section 3 in this case.
The reach from Cross Section 2 to 1 defines the expansion zone downstream of the bride. The higher coefficients are applied to cross section 2 in this case.
At Cross Section 1 and further on downstream, the flow is considered fully expanded, so Cross Section 1 maintains the typical coefficients (0.1 and 0.3).
![clip_image002[4]](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQdLG_hTEqkxyxlw5HXlyPRcj2u4zoXXQ2BjJoEEjkiwtZ_hXmu_x2nsLqCe_Y-yVHm9mqtys_cUkWE1osh8nR-KbEBglVcODu86OKm1rCG0Cyf4fOlOgGFtvlaiywOjgnJZIhX2aQeERW/?imgmax=800 "clip_image002[4]")
Copyright © RASModel.com. 2012. All rights reserved.
In HEC-RAS, it is a well known modeling technique to increase the coefficients of contraction and expansion in the vicinity of a bridge for steady flow modeling.
This is done to capture the energy loss resulting from increased flow contraction approaching the bridge, and increased flow expansion when leaving the bridge. This energy loss is not accounted for in the friction loss, so HEC has added in the ability to account for it using the contraction and expansion coefficients, multiplied by the difference in velocity head between two cross sections. Typically, RAS modelers will apply the higher coefficients (0.3 for contraction, 0.5 for expansion) at Cross Sections 4, 3, and 2 of the traditional cross section layout for bridges (see figure at the bottom of this post). Cross Section number 1 (the most downstream of the 4-cross section layout) is typically left at the default values of 0.1 and 0.3, respectively.
A common question is “why is Cross Section #1 left with the default values?”The coefficients of contraction and expansion are applied to the reach from the cross section at which they are defined to the next cross section downstream. In the energy equation,
, he represents the head loss from one cross section to the next. The equation for head loss, he, is:
Where C is the coefficient of contraction or expansion. Subscripts 1 and 2 represent the two neighboring cross sections. So here you can see clearly that the coefficient of contraction or expansion is applied over a reach, defined by L, which is the length between Cross Sections 1 and 2.
So, for bridge modeling, the reach from Cross Section 4 to 3 defines the zone of contraction as flow approaches the bridge. The higher coefficients are applied to Cross Section 4 in this case.
The reach from Cross Section 3 to 2 defines the fully contracted zone though the bridge. You could make a case that since the flow is fully contracted in this zone, that the typical coefficients should be used (0.1 and 0.3). However, since there is usually a higher amount of turbulence in this zone, traditionally everyone keeps the higher coefficients (0.3 and 0.5). The higher coefficients are applied to Cross Section 3 in this case.
The reach from Cross Section 2 to 1 defines the expansion zone downstream of the bride. The higher coefficients are applied to cross section 2 in this case.
At Cross Section 1 and further on downstream, the flow is considered fully expanded, so Cross Section 1 maintains the typical coefficients (0.1 and 0.3).
![clip_image002[4]](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwWHyYuTKCnLjw8yAZ0f0vWqaeCCJiRwGPxqWO_mQYCp5DDVf1-UqAg1Gmzurv_RInxiPJRKuP7NBG9UPSNVDU7Ij7Y9D7Q1jsts-yx5CwpcEKL6CRdsqqDVTNyEYro3o-UX6l03Ur63G6/s1600-h/clip_image002%25255B4%25255D%25255B4%25255D.jpg "clip_image002[4]")
