A long Channel Consists of Three Parts（Upstream, Middle Stream and Downstream): Hydraulics and Hydrology (Civil Engineering)Assignment, NUS, Singapore

1.A long channel consists of three parts（upstream, middle stream and downstream), and three parts have the same slope of 0.001 and the same geometrical cross-section. The channel bed width is 3. 0 meter, the left bank of the channel is a vertical wall, and the right bank has a slide slope of 2: 1. In the upstream, Manning roughness is 0.035, and the flow is normal flow with a depth of 1.5 meters. The length of the middle stream is 50 meters, and there is 15000 N drag force acting on the flow. In the downstream, Manning roughness is 0.012. (i) Compute the discharge of the flow and the normal flow depth downstream.

Calculate the flow depth at the end of the middle stream(iii) Compute the specific energy values of the flow at the beginning and the end of the middle stream. (iv) Calculate the shear stress values of the normal flow in the upstream and downstream. (v) name the free surface profile between the end of the middle stream and the normal flow downstream. (Hint: Assume that the flow depth at the beginning of the middle sn is the normal flow depth of the upstre位n. The discharge per width can be computed using the average flow width that equals the average of the normal flow top width and the channel bottom width.

2.In the past two decades, a catchment has experienced rapid urbanization. The 10-minute unit hydrographs of. the catchment before and after urbanization are triangular. Before urbanization, the 10-minute unit hydrograph has a peak discharge of 72 m3/s/cm at 30 minutes and a base time of 40 minutes; after urbanization, the unit hydrograph has a peak discharge at 20 minutes and a base time of 30 minutes. (i) Determine the catchment area and the peak discharge of the unit hydrograph after urbanization (ii) Determine the times of concentration of the catchment before and after the urbanization. For a rainstorm given in the table below, the ¢ index values before and after

urbanization the 18 mm/hr and 6 mm/hr, respectively. (iii) Determine and plot the direct runoff hydrographs before and after urbanization. (iv) Comment on the influence of urbanization on the hydrological processes

3. The following table lists the rainfall and direct runoff data in a catchment.
Determine the ¢-index and plot the cumulative infiltration curve. If Horton’s If Horton’s equation is used to represent the potential infiltration curve for the catchment and ic is 20 mm/hr and 5 mm/hr, respectively. In terms of the same

direct runoff depth given in the table, determine the parameter of k in Horton’s equation. The catchment area is 2.4km.

(b) Annual peak discharges at a stream gauging station were given by the table below:

Use the Extreme Value Type I distribution to determine the probability that an
annual flood peak of 35 m3/s will not be exceeded, and to evaluate the return period of the annual peak discharge 50 m3/s. Using Extreme Value Type I distribution and the plotting position method (P m=m/n ), determine the annual peak discharges for 2-year and 10-year return periods, and comment on the results from both the methods.

4. (a) For a region, the 10-year return period ID F of a rainstorm can be represented by the following equation: i=82/(0.36+D)

where i is in mm/hr and D is in hours. For the time interval of 20 minutes use the
above equation to determine and plot a 1-hour design storm profile

(b) A catchment includes two 20-minute isochrone zones. From the upstream to downstream, the areas of both the zones are 1.8 and 0.6 km2, respectively. Use the derived storm profile in (a) to estimate the peak direct runoff discharge from the catchment. The curve number of the catchment is 82. Assume a wet antecedent moisture condition

5. A source of strength 0.2 m3/s.m and a vortex of strength 1 m2/s located at the origin. Determine the equations for the velocity potential and stream function and the velocity components at x = 1 m and y = 0. 5 m. Choose at least five other points and see if streamline(s) can be sketched.

6.Calculate the boundary layer and the displacement thicknesses at the trailing edge of a smooth plate 1.5 m long and 30 cm wide placed in a uniform flow of air with a velocity of 8 is assuming a cubic velocity profile. Calculate also the average drag coefficient and the drag force on the plate. Assume laminar boundary throughout.