SEV322 Hydraulics and Hydrology
Assignment 1, Semester 1, 2011
Due date: 6th April for on and off campus students
The questions carry equal marks and the assignment is worth (5%) of the total assessment.
Q1.
Out of a long-term record of precipitation for four adjacent stations you find that records of one station are missing for the spring months, September, October, and November of a given year. For those three months the other three stations recorded the following total depth in millimetres.
Month / Station 1 / Station 2 / Station 3September / 55 / 65 / 75
October / 47 / 50 / 45
November / 45 / 40 / 55
Estimate the missing precipitation if the long-term average precipitation for the three months in all four stations is
Month / Station 1 / Station 2 / Station 3 / Station 4September / 60 / 65 / 70 / 67
October / 50 / 55 / 65 / 60
November / 45 / 47 / 60 / 55
Note that the station 4 is the station with missing records.
An alternative way of estimating a missing record is by weighting observations by the inverse square distance to the point of the missing record. If the distance of the station 4 from stations 1, 2, and 3 are 5 km, 1 km, and 10 km respectively, compute the missing records.
Q2.
(a) Discuss how the Penman's theory differs from the empirical aerodynamic formula in the estimation of evaporation from free water surfaces.
Penman's formula: E = ( Qn. + Ea.) / ( + )
Aerodynamic formula: E = f(U) (eas - ea )
(b) Estimate the mean daily evaporation from the following data:
Mean air temperature = 18o C
Mean relative humidity = 60%
Daily wind run on that day, U = 260 km
Net energy available at free water surface = 7.94 MJ/m2/day
The empirical aerodynamic formula is given by E = (1.3 + 0.016U) (eas - ea )
where, U is in km/day, es and ea in kPa, and E in MJ/m2/day.
Take the value of as 0.066 kPa /oC.
Q3.
Rainfall intensities for every 10 min increments of a 60 min storm is given in sequence as: 102, 78, 90, 72, 56 and 45 mm/hr.
The infiltration capacity for the given soil type and cover is known to decrease at the following rate:
Time in min / 0 / 10 / 20 / 30 / 40 / 50 / 60Infiltration capacity in mm/hr / 100 / 75 / 56 / 44 / 35 / 29 / 25
Determine
(a) the surface runoff for every 10 min increments
(b) the runoff volume for the storm
(c) - index for the storm. Infiltration capacity at the start of the storm may be assumed as 100 mm/hr.
Note: The area under the infiltration capacity curve may be computed using the trapezoidal rule for every 10 min increments.
Q4.
(a)
The following data were collected for a stream at a gauging station. Compute the discharge in the stream.
Distance from one end of water surface / Depth of water(m) / Velocity at 0.6d
m/s / Velocity at 0.2d
m/s / Velocity at 0.8d
m/s
0 / 0 / - / - / -
1.2 / 0.7 / 0.4
2.4 / 1.7 / 0.7 / 0.5
3.6 / 2.5 / 0.9 / 0.6
4.8 / 1.3 / 0.6 / 0.4
6.0 / 0.5 / 0.35
7.2 / 0 / - / - / -
(b)
The following data were obtained by stream gauging of a river:
Main gauge staff reading (m)12.0012.00
Auxilliary gauge staff reading (m)11.6511.02
Discharge (m3 / s) 9.5015.20
What should be the discharge when the main gauge reads 12 m and the auxiliary gauge reads 11.37 m ?
Q5.
The 1 hour unit hydrograph (1 cm rainfall excess) for a watershed was determined to be approximately as follows:
(a) Determine the area of the watershed
(b) Plot the hydrograph of flow from a 2 hour storm in which 5 mm of rainfall fell during first hour and 6 mm during the second hour. Assume a uniform loss rate of 3 mm /hr and neglect base flow.