CE444-APPLIED HYDRAULICS
SPRING 2016
FIRST MIDTERM
FEBRUARY 26, 2016 1500-1550

Name: ______________________ Red ID ___________________ Grade: _______

Instructions: Closed book, closed notes. Use engineering paper. When you are finished, staple your work in sequence (1 to 5), and return this sheet with your work.

  1. (25%) A 100-acre watershed has two distinct subareas: (1) an undeveloped portion, of 35 ac and runoff coefficient C= 0.3, and (2) a developed portion, of 65 ac and C = 0.7. If the 10-yr rainfall intensity is 0.5 in/hr; what is the peak flow by the rational method? Calculate the exact value (in cfs), using the appropriate unit conversions.

    Qp = C I A = I Σi (CiAi) = 0.5 in/hr × [(0.3 × 35 ac) + (0.7 × 65 ac)]

    Qp = 0.5 in/hr × 56 ac × [1/12 ft/in) / 3600 s/hr] × 43560 ft2/ac = 0.5 × 56 × 1.00833

    Qp = 28.23 cfs.

  2. (25%) A rectangular channel is to be designed to convey 100 cfs. The bottom width is b = 10 ft, the bottom slope is So = 0.001, and the Manning's n = 0.013. Calculate the design flow depth (3 significant digits) using trial and error.

    Manning equation:

    Q = (1.486/n) A R2/3 S1/2

    Q = (1.486/n) A5/3 S1/2 P-2/3

    Try y = 1 ft.

    Q = (1.486/0.013) 105/3 × 0.0011/2 12-2/3 = 32.01 cfs.

    Try y = 2 ft.

    Q = (1.486/0.013) 205/3 × 0.0011/2 14-2/3 = 91.70 cfs.

    Try y = 2.1 ft.

    Q = (1.486/0.013) 215/3 × 0.0011/2 14.2-2/3 = 98.53 cfs.

    Try y = 2.12 ft.

    Q = (1.486/0.013) 21.25/3 × 0.0011/2 14.24-2/3 = 99.91 cfs.

    Try y = 2.13 ft.

    Q = (1.486/0.013) 21.35/3 × 0.0011/2 14.26-2/3 = 100.6 cfs.

  3. (25%) A rectangular channel has a discharge q = 2 m3/s/m. What is the critical depth? What is the critical velocity?

    yc = [q2/g]1/3

    yc = [22/9.81]1/3

    yc = 0.742 m

    vc = q / yc = 2 / 0.742 = 2.697 m/s

  4. (25%) Please answer questions in a brief statement.

    1. What is the time of concentration? In the most general case (Papadakis formula), what four physical variables is it a function of? Which two variables are in the numerator? Which two are in the denominator?

      The time of concentration is the time required for a drop of water to travel on the land surface, from the most distant point in the watershed to the outlet.

      In the Papadakis formula, the time of concentration varies as a function of length L, slope S, rainfall intensity i, and roughness factor n.

      Time of concentration is directly proportional to L and n, and inversely proportional to i and S.

    2. What is the difference between the Manning and Chezy equations? State three differences.

      1. In the Chezy equation, hydraulic radius R is elevated to the 1/2 power. In the Manning equation, R is to the 2/3 power.

      2. The Chezy coefficient appears to be dimensional, but can be readily converted to dimensionless form. On the other hand, the Manning coefficient appears dimensionless, but it is not (a 1.486 unit conversion coefficient is applicable in U.S. Customary units).

      3. The Chezy equation is theoretical; the Manning equation is practical.

      4. The Chezy equation was developed in 1776; the Manning equation in 1889.

    3. What four forces are normally present in open-channel hydraulics? What two of these forces are present in hydraulic jump analysis? Why?

      Gravity, friction, pressure gradient, and inertia.

    4. What are the maximum and minimum values of Manning's n that can be achieved in practice?

      Everglades modeling: n = 1.000; lucite (acrylic plastic): n = 0.008.

    5. Is it correct to say that the Chezy coefficient varies with the hydraulics radius, and that the Manning coefficient is a constant?

      Yes, indeed the Chezy coefficientt may vary with the 1/6 power of the hydraulic radius; but the Manning coefficient is not a constant. It varies with the flow stage, flow level, and consequently, with the prevailing form of bed roughness.