Lesson 14 Storm Drain System Design (3) -

Calculating Roof Area for Roof Drain Sizing

by Anjian Lu, CPD

THE DILEMA

Plumbing engineers often work on projects that, because of location, are governed by different plumbing codes. Variations among the codes sometimes cause confusion and present challenges either within the design group or between the designer and the plan reviewer or inspector.

The roof area calculation for sizing roof drains is an example of how differences among the codes can challenge the designer. We all agree that vertical walls contribute flow to roof drains because they collect rainwater when winddriven rain hits and runs down the wall, but how do vertical walls affect the sizing of roof drains? The codes differ in their answers to this question.

CODE SEARCH

A search of the national codes found the following references to the calculation of roof area for sizing roof drains.

THE THREE MODEL PLUMBING CODES ADDRESS THIS ISSUE AS FOLLOWS:

National Standard Plumbing Code (NSPC)

13.1.10.3 Vertical Walls: Where vertical walls drain onto roofs, an allowance based on 50 percent of the maximum projected wall area shall be added to the roof area onto which each wall drains.

International Plumbing Code (IPC)

1106.4 Vertical Walls: In sizing roof drains and storm drainage piping, one-half of the area of any vertical wall that diverts rainwater to the roof shall be added to the projected roof area for inclusion in calculating the required size of vertical conductors, leaders, and horizontal storm drainage piping.

Uniform Plumbing Code (UPC)

1106.4 Side Walls Draining onto a Roof: Where vertical walls project above a roof so as to permit storm water to drain to the roof area below, the adjacent roof area may be computed from Table 11-1 as follows: 1. For one wall, add 50 percent of the wall area to the roof area figures. 2. For two adjacent walls, add 35 percent of the total wall areas. 3. For two opposite walls of the same height, add no additional area.

As you can see, NSPC requires 50 percent of the maximum projected wall area to be added to the roof area calculation.However, the designer must project the wall area in different directions and take the maximum area.

IPC tells you to add one-half of the area of any wall that diverts rainwater to the roof to the roof area. Here, any means all.

UPC’s guideline is much more clear and executable. I’ll explain why UPC set the table this way.

GEOMETRY IN ROOF AREA CALCULATIONS

Rain gauge
Figure 1 Rain gauge. Source: CoCoRaHS

First, rainfall density is measured by a rain gauge (see Figure 1), which consists of three parts: a cylindrical overflow tube, a funnel on top, and a measuring tube underneath the funnel. The funnel diverts water into the measuring tube, which is one-tenth of the area of the funnel top for more accurate reading. The overflow tube stores water when the measuring tube is full and overflows. (Imagine that the funnel top is part of the roof.)

Let’s look at a real roof as an example.

Figure 2 shows a simple roof with projected high roofs. The four roof drains in this roof are A, B, C, and D. Roof drains A and C are the same and have two perpendicular walls. Roof drain D has one vertical wall, and roof drain B has two opposite walls.

plan
Figure 2 Example roof and roof drains

Suppose rain hits the wall in angle α. We then can draw a triangle acd. Its three sides are ad, dc, and ca. We express their length with an upper score in the functions to follow.

Let’s look at the horizontal roof draining to roof drain C first. If the wall length is Lc and the area is Ach, then:

Now, what about the wall north of roof drain C? If there is no wall on the west, the answer is as simple as taking one-half of the area of the wall since wind direction is unpredictable.

UPC suggests using 35 percent of the total area of both walls. In most situations, this is reasonable because rain hits both walls at a 45-degree angle (i.e., HV = ½H x sin(45) = 0.5 x 0.707 = 0.3536 or 35 percent). However, if one of the walls is much larger than the other, the drain may be undersized. On the other hand, if you take 50 percent of the total area, the drain may be oversized. For this reason, the NSPC’s guideline, which requires using 50 percent of the maximum projected area, may be the best solution.

formulas
Figure 3 Equations

As for areas with opposite walls, such as the area for roof drain B, UPC’s guideline No. 3 of adding no additional area to the calculation is adequate. However, if the two walls are not of the same size, the difference between the two areas should be added. As you can see from Figure 1, the funnel of the rain gauge can be considered as a round 360-degree wall in the periphery of the building roof. The rainwater recorders do not take the roof geometry into account, so we, as engineers, should.

SUGGESTIONS

Based on the analysis above, I offer the following suggestions for your consideration.

For Single Roof Drains

For a single vertical wall affecting the collection area of a roof drain, add 50 percent of the side area to the total for calculating the flow rate.

For a single curved vertical wall, use 50 percent of the maximum projected area.

For multiple walls, use 50 percent of the maximum projected area of all walls.

For drain areas between two opposite walls, add no additional area. If the area of each wall is not the same, add 50 percent of the difference between the two walls.

For Horizontal Pipes or Leaders Receiving Two or More Roof Drains

Use only 50 percent of one maximum total projected side area of the walls in one direction.

For the Entire Roof of a Building

Do not add any side wall area except when the projected wall area is falling off the roof boundary. To decide this, use the architectural elevation drawing to draw a 63-degree line starting from the top of the highest wall (the hypotenuse of a right triangle with bottom length of 1 and height of 2). Add 100 percent of the horizontal area falling off the roof boundary to the total horizontal roof area for sizing the building rainwater drain.

For Riser Diagrams

We may not need to put the exact arithmetic sum of the branches to a main or submain. This is because when a wall may affect one part of the piping, it may not affect the downstream part as mentioned above.

CONCLUSIONS

Properly sizing the roof drainage system is very important for structural safety, so the importance of calculating roof area cannot be overlooked. Thus, a uniform method in all the plumbing codes nationwide is a request of plumbing engineers like me.

With 3D MEP AutoCad or Revit increasing in popularity, it should not be difficult to determine the correct projected area for sizing the rainwater system, including the roof drains, leaders, gutters, downspouts, and horizontal piping. (作者介绍及照片略)

Vocabulary

contribute贡献,添加
winddriven 被风吹动的
differ不同,相异,意见不一
model模范,典型,模型,型号
address演讲,阐述
vertical wall垂向的墙(不垂直的墙会塌掉)
allowance补贴,余量
divert转移,转向,导向
project工程,项目;突出;投影
projected roof area屋面的(水平)投影面积
maximum projected wall area 墙壁最大投影面积
inclusion (in)包括
adjacent相邻的
compute计算
opposite walls相对的墙,相平行的墙
guideline准则,导则,规定
executable 可执行的
geometry几何学
rain gauge雨量筒
cylindrical 圆柱形的
overflow tube(雨量筒的)溢流筒
funnel漏斗
measuring tube(雨量筒的)测量筒
underneath在。。。之下
imagine设想,想象
high roof高屋顶,高屋面
perpendicular垂直的
suppose假定
upper score(文字)上方的横杠,上划线
unpredictable 无法预测的
periphery圆周,周边
analysis分析
offer提供
for someone‘s consideration供某某人参考
curved vertical wall曲线型的垂向墙
multiple walls多道墙
falling off ...落到。。。之外
boundary界限,边界
hypotenuse(直角三角形的)弦,斜边
right triangle直角三角形
arithmetic sum算术和
downstream part 下游部分
conclusion结论
overlook忽视
request请求
3D MEP AutoCAD三维的MEP AutoCAD
Revit 一种三维的绘图软件和方法
gutter天沟
downspout落水管

第14课 雨水系统设计(3)

确定雨水斗管径时屋面面积的计算

进退维谷

由于地点不同,建筑给水排水工程师常常从事由不同规范管辖的工程。各种规范之间的差异常常引起混乱和在设计班子内部或在设计者与图纸审查者或施工检查员之间出现异议。

用来确定雨水斗管径的屋面面积计算就是规范之间的差异挑战设计者的一个例子。我们大家都同意垂向的墙壁增加流到雨水斗的流量,因为雨水在风的作用下落到墙上并且沿墙流下。但是,究竟垂向的墙壁是如何影响雨水斗尺寸的呢?不同的规范对这个问题有不同的答案。

各种规范的比较

查阅国内的各种规范后发现,在确定雨水斗管径的计算有如下的参考条文:

三种主要的建筑给水排水规范对这项内容的规定如下:

美国国家标准建筑给水排水规范(NSPC)

13.1.10.3 垂向墙壁:当垂向墙壁上的雨水排到屋面上时,墙壁最大投影面50%的面积必须加到每道墙排水到该屋面的面积内。

国际建筑给水排水规范(IPC)

1106.4 垂向墙壁:在计算雨水斗和排水管管径时,任何将雨水排到屋面的垂向墙壁,其一半的面积必须加入屋面的(水平)投影面积内,以便在计算室内外雨水立管和水平排水管时计入。

统一建筑给水排水规范(UPC)

1106.4 排水到屋面的侧墙:当垂向的墙从屋面突出并允许将雨水排到下方的屋面上时,相邻的屋面面积可以按表11-1来计算如下:1. 只有一道墙时,加整墙面积的50%到屋面的面积数中。2. 当有两堵相邻的墙(译注:指成直角的两道墙)时,加两道墙总面积的35%。3. 当两道墙相对且高度相同时,(中间的屋面)不外加面积。

可以看出,NSPC要求将墙的最大投影面的50%加入到屋面面积的计算中。可是,设计者必须将墙面往各个方向投影,取最大数。

IPC告诉您将把雨水排到屋面的任何墙的面积的一半加到屋面面积中。

UPC的规定清晰得多。我将解释UPC为什么将表格设计成这样。

屋面面积计算几何学

首先,降雨强度是由雨量筒测定的(见图1)。它由三部分组成:圆筒状的溢流筒(overflow tube)、顶部漏斗(funnel)和量筒(measuring tube)。漏斗将雨水导入到量筒中,为了准确起见,它(的横截面积)是漏斗口面积的十分之一。当量筒中的水满溢流时,溢流筒将水储存起来。(想像漏斗口是屋顶的一部分。)

Rain gauge
图1 雨量筒F

让我们看一个屋面的实际例子。

图2表示一个有突出部分的简单屋面。四个雨水斗分别为A、B、C和D。雨水斗A和C相同并有两堵垂直的墙。雨水斗D有一道墙,而雨水斗B有两道相对的墙。

设想雨以α;的角度打到墙上。我们然后可以画一个三角形acd。它的三条边分别是ad、dc和ca。在下面的方程式中,我们将它们的长度以边名上方加横线表示。

我们首先看排入雨水斗C的水平屋顶。如果墙的长度是Lc,而面积为Ach,那么:

plan
图2 屋面和雨水斗的例子

那么,位于雨水斗C北边的墙应如何考虑?如果西边没有墙,答案很简单:加上一半的墙面积,因为风的方向是不可预测的。

UPC建议采用两道墙总面积的35%。在大多数情况下,它是合理的,因为雨以45堵的角度打到墙上(即:Hv = 1/2H x sin(45)= 0.5 x 0.707 = 0.3536,或35%)。但是,如果一道墙的长度比另一道墙长得多,那么雨水斗就可能被低估了。另一方面,如果你取总面积的50%,雨水斗就可能被高估了。为此,NSPC的最大投影面积的50%规定,可能是最好的解决方案了。

有关相对墙壁的面积,如雨水斗B的面积,UPC的第三条规定,即计算中不加面积,就可以了。但是,如果两道墙的尺寸不一样,则两墙面积之差,就应计入。从图1可以看出,雨量筒的漏斗可以被看作是建筑物周边360堵的墙。雨水记录仪不考虑屋顶的几何形状,但是我们工程师应该。

formulas
图3 方程式

建议

根据上述的分析,我提出下述建议供您考虑。

对于单个雨水斗

只有一道墙影响一个雨水斗的集水面积时,加入50%的墙面积。

只有一道曲线的墙时,使用50%最大投影面积。

对于多道墙,使用所有墙最大投影面积的50%。

对于夹在相对两道墙中间的雨水斗,不加面积。如果每道墙的面积不一样,加入两墙面积的50%。

对于接纳两个或多个雨水斗的水平管道或者立管

只加一个方向最大投影总面积的50%。

对于建筑物的整个屋面

除非投影的墙面积落在屋面界限以外,不要将任何侧墙的面积。为了确定这一点,使用建筑立面图,从最高一道墙的顶部开始画一条63度的线(即底边为1,高为2的直角三角形的斜边)。将100%的落在界外的水平面积加入到屋面水平总面积中来确定建筑物雨水排水管。

对于系统图

我们可不必将各支管的算术和加到干管或支干管中。这是由于当一道墙会影响一段管道时,它可能不会影响下游的部分。(见前面所述。)

结论

正确确定屋面排水系统的管径对结构的安全性有重要意义。所以,计算屋面面积的重要性不可忽视。所以,像我这样的建筑给水排水工程师要求在国内使用的各种建筑给水排水规范使用统一的方法。

随着三维的AutoCAD和Revit的逐渐推广,应该不难确定正确的投影面积来合理地选用雨水排水系统的管径,包括雨水斗、雨水立管、天沟、落水管和水平管道。

Questions:

  1. How much allowance shall be added to the roof area based on NFPC if vertical walls drain onto roofs?
  2. What does "projected roof area" mean according to 1106.4, IPC?
  3. In the article, the word "project" is used many times, such as: "projects", "projected wall area", "projected roof area", "walls project above a roof", "projected high roofs", "total projected side area". Can you figure out its difference meanings in these phrases?
  4. What is the difference between "projected wall area" by NSPC and "projected roof area" by IPC?
  5. Why add 35 percent of the total wall areas to the roof area if two adjacent walls divert flow to a roof?
  6. Why additional area should not be added for two opposite walls of the same height if a drain is between them? How about two walls with same height but difference length?
  7. How much area would you add to the roof area if a wall is curved as a semi-circle?
  8. If there are two opposite walls, one is on the edge of the north side and another on the south edge, do they affect the flow at the building storm drain outlet? (Suppose there is only one outlet.)
  9. Why do we need add only the projected horizontal area of a wall or walls off the roof boundary with 63 degree angle to the calculation for the entire roof of a building?
  10. How do you get a 63 degree angle if you do not have a protractor?

References:

  1. Overcome Code Challenges - Calculating Roof Area for Roof Drain Sizing, by Anjian Lu, CPD, Plumbing Systems & Design, ASPE, June 2009, 2009

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