Creative Answers For Curious People

I’m in the process of writing a book “Creative Answers For Curious People”. It’s a number of life’s questions I’ve had and wasn’t satisfied with the answers available. The questions may arise from something I’ve seen on television, read somewhere, or observed. For example, can an asteroid on a collision course with Earth be deflected? I decided to use some basic physics to help develop an answer that would satisfy me. I enjoy doing these type calculations on a wide variety of subjects.

The potential audience for the book is very select and is basically for people who enjoy science and are too curious for a generic answer to a question. So, over the next several months I’ll periodically be adding a question with an answer that satisfied my curiosity. Presently I have over 132 curious questions and answers which I seem to add to every month.

I’m going to test interest by printing a few. If you find this interesting, please drop me a note and I’ll keep adding them. I hope you enjoy them.

Books Sections

6.9  Why Didn’t My House Flood?

During August 2017, Hurricane Harvey came through Houston, Texas. My home in Kingwood, Texas was spared but many of my friends’ homes and businesses flooded. It is estimated that 3,300 homes were flooded in Kingwood. I wanted to know how safe my location was. Being in a 500-year flood plain, which flooded twice, wasn’t something I could relate to.

There was much speculation on why the flooding occurred and why Lake Houston rose so much. Doing some research shows that there are many tributaries feeding into Lake Houston besides Lake Conroe but Lake Houston has only one outlet. Figure 6.9.1 shows the flow in (Qin) and flow out (Qout) and Lake Conroe is part of the (Qin) West Fork.


Figure 6.9.1 Lake Houston And Tributaries

Consider Lake Houston with the peak input flows (Qin) from Lake Conroe and its tributaries as shown on Figure 6.9.2 and the outflow (Qout) from Lake Houston also known from published data.

Now, when the input flow is equal to the output flow a steady state condition is reached and the height of the lake will remain constant. However, when more is going in than is going out the water continues to rise in the lake and builds up with time.

One thing that concerned me was why locations far from the lakes shore within Kingwood flooded. Viewing drone footage after the storm answered this question. The interior locations can flood when they are near creeks, lakes or water drainage bayous connected to the lake. Since water seeks its own level, these waterways will rise as the level of the lake rises.

Hurricanes move through the watershed area (Arain) at  ( Vmph) and deposits rain at ( r ft/sec). This rain flows into tributaries and into the West and East Fork San Jacinto River. It goes into Lake Houston and out the Lake Houston dam and spillway. When what enters ( Qin ) from the San Jacinto is greater than leaves (Qdam) from the spillway, Lake Houston will rise above its normal pool level of 43 feet.

Figure 6.9.2  shows the water shed and depressed basin type area (Abasin ) and spillway.



Figure 6.9.2  Flooded Basin Area

The surface area (Arain ft2) is the area that captures the rainfall and directs it to the lake and is called the rain shed area. The water height (h ft) in Lake Houston (Abasin ), is the height above the normal lake pool level of 43 feet. When the water into the lake is more than the water out of the lake, then (h) starts to build up with time (tmin). The theory is much like filling up a bathtub. When the water going in, meaning the faucet or rainfall from the watershed, is greater that the water going out, meaning the drain or spillway, the level ( h ft ) will be stored and build up in the basin with time.

The Lake Houston spillway is a weir type dam which is uncontrolled and can build up (h) above the normal pool level. There are two smaller Tainter gates which are controlled release dams and have a total capacity of about 10,000 cfs (cubic feet per second). The Lake Conroe dam is from another water shed area and releases into the W. San Jacinto at 79,000 cfs. With this information an analytical model can be built.

To determine the amount of flow into the lake, consider that the hurricane has to pass through the watershed area at Vmph and it is 200 miles in diameter. The time the rain will be on the area is :

t = 200 miles/ Vmph   hrs.

Hurricane Harvey was a slow mover at 2 mph so it took 100 hrs. or 4 days to get through. It deposited 48 inches of rain during this time or  r =1.2*10-5 fps

The water going on the rain shed area (Arain) of about 1,200 mi2  (  3.3*1010 ft2 ) in cubic ft per second (cfs) and into Lake Houston;

Qin = Arain*r  + (flow from Lake Conroe) cfs

The build-up above the weir (h ft) using weir analysis, as discussed in Section 6.10 is ;

Qweir = Cw*L*(2*g)1/2 * h3/2 cfs

What goes into Lake Houston minus what comes out will be stored in the lake meaning basin;

Qin - (Cw*L*(2*g)1/2 * h3/2+Tainter gates)=Abasin*h/tsec (Eq 1)

The height (h) above the normal level can be solved for using (Eq 1) and iterative means.

hflood=43+h ft. The height (h) can be solved using equations (1).

hflood = 43 + h ft.

As long as home or business elevations are above the flood height (hflood), flooding of that location shouldn’t occur.

Lake Houston’s surface area is about 18.5 mi2  ( use Abasin = 5.5*108 ft2 ). This analysis considers the lake as it expands which is the dashed line in Figure 6.9.1.

During a 4-day period the level above the normal lake level is (hflood) = 43+10 = 53 ft.

This rise flows onto the land and raises streams and drainage bayous.

Using the data of Table 6.9.1 and performing the calculations:

Source

Peak Flow Rate
(cfs)

Calculated Pool Level Rise Lake Houston
4 days

Dam Lake Conroe

79,141

-

Tributaries Into Lake Houston

365,059

-

Dam Lake Houston

425,000

53.0 ft

Table 6.9.1 Flows And Rise Of Lake Houston

Table 6.9.2 shows how this information of a 10 ft rise (h) in 4 days can be used by knowing the elevation of locations. There are obvious errors after viewing drone footage of partially submerged cars. Town Center and H.E.B had at least 3 ft of water not the 1 ft calculated. Local differences in elevation than published may have been partially responsible along with the simplicity of the analysis method. From the actual observed data, it appears that flooding seems to occur when the lake level is greater than 56 ft.

Location

Elevation Above Lake Houston

Status
Drone View*
(Calculated)

Calculated Water Rise at Location
*(actual)

**1. Walmart Northpark Dr
**(number on Figure 6.9.1)

76 ft

Not Flooded*
(53 ft)

0 ft
*(0)

2. Kroger Northpark Dr

75 ft.

Not Flooded*
(53 ft)

0 ft
*(0)

3. Sandy Forks Drive

75 ft.

Not Flooded*
(53 ft)

0 ft
*(0)

4. Wendy’s L. Houston Pkwy

62 ft

Not Flooded*
(53 ft)

0 ft
*(0)

5. Barrington

52 ft

Flooded*
(53 ft)

1 ft
*(4 ft+)

6. Kingwood High School

49 ft

Flooded*
(53 ft)

4 ft
*(4 ft+)

7. Town Center Kingwood           

52 ft

Flooded*
(53 ft)

1 ft
*(3 ft+)

8. Summerwood
   Mallard Lane

52 ft

Flooded*
(53 ft)

1 ft
*(2+ft)

9. H.E.B. Kingwood
 Lake Houston Pkwy

52 ft

Flooded*
(53 ft)

1 ft
*(3 +ft)

10. Bear Branch Library Bens View Loop

52 ft

Flooded*
(53 ft)

1 ft
*(3 ft+)

11. Foster Mills pool area Elk Creek

51 ft

Flooded*
(53 ft)

2 ft
*(3 ft+)

12. Sharky’s

49 ft

Flooded*
(53 ft)

4 ft
*(6 ft)

13. Cedar Landing Marina Huffman

48 ft

Flooded*
(53 ft)

5 ft
*(6 ft +)

Table 6.9.2 Kingwood Elevations And Status During Hurricane Harvey

Hopefully this amount of rain won’t happen again.

Summary:

A simplified analysis can determine the flood height expected near the lake.

The analysis allowed me to understand what was occurring. The amount of rain from the stalled storm on an average of 12 inches per day for 4 days was just too much for the present flood control system for this area to handle. As a friend mentioned, Lake Houston was designed as a water supply for Houston, not for flood control. To have the Lake Houston dam used for flood control, more Tainter gates would have to be added to handle the additional flow. Local flooding due to a heavy rain is different and discussed in Section 6.11.

6.10  Why Does Lake Houston Rise Above The Spillway?

This was a question that came to me after writing Section 6.9 since the flooding height (h) depended on these flow rates. How does the lake get higher than the top of the spillway and not just pour over it?

It’s all based on the dam and its spillway design. A spillway is simply a low dam of a certain height (s), which allows water to flow over the top (h) as shown on Figure 6.10.1.


Figure 6.10.1 Flow From Lake Houston Dam

In addition to the spillway, which is an uncontrolled flow, water can be released in a controlled manner with two 18 ft x 20.5 ft Tainter radial swing gates shown on the right. The spillway is called a weir in engineering terms and can be used to measure flows.



Figure 6.10.2 Spillway Weir Flow

Figure 6.10.2 shows the flow over the top of the spillway (s) or weir and why the lake level builds up (h) with more flow into it. The flow rate can be calculated from:

Qweir = Cw*L*(2*g)1/2 *h3/2 cfs

The flow rate out of two Tainter gates is;

QTainter = 10,000 cfs

The maximum flow out of the dam with both gates open is therefore;

Qout = Qweir + QTainter

Summary:

An approximation of the flow rate out of a lake, which contains a spillway/weir can be made using the change in height rise of the lake above the spillway/weir.

6.11 What Caused The Street To Flood

During heavy rainstorms in Texas, flooding occurred in front of some homes that hadn’t flooded before. This flooding was not due to the overfilling of Lake Houston. Concern was that the underground storm sewer lines had become plugged with debris. There are several miles of these underground lines. I wondered if it might have been because of the 6 inches per hour (iph) of rain that fell for an hour. It may have been too much for the storm sewer drains to handle. Such rains are rare and the amount of flooding that occurred hadn’t happened in the past. The question was if the drains were plugged or was it just due to the sudden high rainfall rate. Figure 6.11.1 shows the flooded area.



Figure 6.11.1 Flooded Area In Front Of Homes

A simple analysis can help answer this question. Figure 6.11.2 shows a depressed basin type area (Abasin ) with the storm sewer drains in the flooded area.




Figure 6.11.2 Flooded Basin Area

The surface area (Arain ft2) is the area that captures the rainfall and directs it to the drains and is called the rain shed area. The roads are designed to flood but not build up above curb level to house level. When the rain water height (h ft) in the basin (Abasin ), which is a low point, reaches a height above the curb drain the water starts to build-up. The drains are basically curb type drains with a flow area of (Acurb ft2) and there are (N) number of them in the basin area. The rainfall rate is (r ft/sec) whose duration is (tsec). With this information an analytical model can be built. The theory is much like filling up a bathtub. When the water going in, meaning the faucet or rainfall from the watershed is greater that the water going out, meaning the drain or storm sewers, the level ( h ft ) will build up in the basin and rise (h) over time (tsec).

The water going into the basin;

Qin = Arain*r   cfs

The water going out of the drains due to gravity alone is (1);

Qout = 0.8*N*Adrain*(2*g*h)0.5  cfs

When the difference between the flow in (Qin) is greater than the flow out (Qout) the build-up (h) over a time period (tsec ) will occur.

Qin - Qout = (Abasin )* h/tsec

Arain*r - 0.8*N*Adrain*(2*g*h)0.5 = (Abasin )* h/tsec

This equation can be solved for (h) using iterative methods or a closed form solution.

During the storm N= 2, Acurb = 2.0 ft2, Arain=320,000 ft2, Abasin = 25,000 ft2, r = 1.4*10-4 ft/sec (6 in/hr), g= 32.2 ft/sec2 , tsec = 3,600 sec (1 hour)

Table 6.11.1 shows results;


Condition

Flow entering Qenter

Flow leaving Qleave

Result
hft

Heavy rain 6 iph

44 cfs

34 cfs

1.7 ft build up

Normal rainfall 3 iph

22 cfs

18 cfs

0.5 ft build up

 

Table  6.11.1 Flow Model Results

These results show that a flooding situation occurred with 6 inches per hour (iph) as was observed. The drains just couldn’t handle 6 iph for an hour of rain and the level built up. Normal heavy rainfall of 3 iph doesn’t appear to build up higher than the curb.

Some idea if the drains were plugged can be determined by observing how long it takes for the basin to empty after the rain had stopped.

Qdrain = 0.8*N*Adrain*(2*g*(h/2))0.5  = 24 cfs

(t) time to drain = Abasin*hfinal/Qdrain = 1,800 sec or about 1/2 hour.

The site was dry again in less than an hour, meaning it had drained near the capacity it should due to gravity alone. This suggests that the drains were acting as they were designed and probably weren’t plugged. It appears that the heavy rainfall and not plugged drains was what had caused the flooding.

Summary:

The storm sewer drains can’t seem to handle 6 inches of rain in an hour and build up to almost 2 feet. They have not built up with 3 inches of rain in an hour. Since they drain quickly, they are probably not plugged.