Hydrology EESC BC 3025

HYDROLOGY - Homework # 5

1) (10 points) The streamflow of a small river in Colorado has been measured by the wading technique that you can see in Fig 4.11 (page 91/92) in our textbook (I actually did the measurements by myself!). First, we put a rope across the river to mark the cross section where we wanted to do the measurements. Then we waded across the river and took one reading in 60% of the depth every 1 to 2.5 foot (for deeper rivers, you would use two measurements, such as in Fig 5.23). The total width of the river was 26.1 feet. We counted the number of revolutions of the current meter for a certain amount of time.

Download the data table (file:co_q.csv, "csv" stands for "comma separated values" can be imported into EXCEL). The flowmeter has been calibrated: 1 revolution/s is equivalent to a flow velocity of 2.2 ft/s. Use the data in the table to calculate the flow velocity and put the result into the next column. Then calculate the area for which the measurement is representative (depth * width). Finally calculate the discharge rate for each section and sum them up to obtain the discharge rate in the entire river.

2) (4 points) Laminar flow table

Please describe in a couple of short paragraphs what we did with the laminar flow table and how the results relate to Bernoulii's law. Look again at the outline of the excercises we did.

3) (8 points) Weir experiment
This table (VWeir_2_20_07.xls) contains data obtained with the Weir experiment in Mudd. Plot the discharge rate Q as a function of H^2.5. Do it with the data of both groups. Set the intercept to 0 and determine the slope of the graph (this is an option when you fit the data with a line). How well do the data plot on a straight line? Do you have any explanantion for the datapoints that do not fit the general trend? What value did you obtain for the experiments for C_d? (g=9.81 m s^-2). Watch the units!

4) (6 points) Reynolds number
Calculate the Reynolds number for the NYC water tunnels, assuming an inner diameter of 24ft. There are two of these tunnels in operation, determine the flow velocity from the amount of water used in the city. The city uses ~ 1.1 billion gal/day. Is the flow turbulent or laminar?

5) (12 points) Flood estimate
A construction project is planned for a small non-monitored stream near Oracle Arizona. This stream is typically dry during most of the year, but floods during extreme presipitation events. The planning agency is concerned that their construction site might be flooded during extreme year and wants to know how high the water might be able to rise in the stream. One way is to estimate the maximum amount of precipitation to be expected in a day, assume that all the water makes it into the stream (no evaporation) and then convert the discharge rate into a depth using Manning's equation.

Info you'll need:

size of the watershed: 42.3 miles²
streambed is rocky, the roughness coefficient was estimated as 0.05
the stream bed drops in elevation at a rate of 2m per 100m
daily precipitation data, Oracle, AZ, 1984-91
Manning's equation:

a) Make a histogram of the daily precipitation data. Is the parameter normally distributed? If it is, determine the precipitation rate exceeded once in a hundred years, if not use the maximum precipitation rate in the record as best estimate for the worst case scenario.

b) Calculate the maximum discharge in the stream assuming that all that precipitation comes down and enters the stream in 2 hours. Express the result in metric SI units.

c) Assume that the channel has a V-shape cross section, with a 90^o angle at the bottom (draw a little sketch). Let us call the length of the sides of the "V": L and the depth of the channel: h. Then R_H = area/wetted perimeter = L²/(2*2*L) = L/4. Remember that Q=A*U, with A being L²/2. Rearange Mannings equation to get L. Then convert L into h, using L² = 2h², valid for this particular triangle. So, how deep can the stream get and how far from the center do you need to be in order to avoid flooding?