CE322 Basic Hydrology

Jorge A. Ramirez

 

Midterm Exam No.1 - Solution

 

Problem 1   Define, list, and/or explain the following:

a)      Define Hydrologic Cycle: idealization of the process of water transport and redistribution throughout all the components of the physical climate system. List and define the main components of the Hydrologic Cycle: precipitation, evaporation, transpiration, surface runoff, groundwater runoff, infiltration, and storage.

b)      Define: partial pressure: in a mixture of ideal gases, partial pressure is the pressure exerted by each of the individual gasses; precipitable water is the vertically integrated total mass of water vapor per unit area for a column of atmosphere. Precipitable water represents an upper limit to the total amount of precipitation that may be realizable from the given atmospheric column.

c)      Define: interception: fraction of the gross precipitation that is intercepted by the canopy of vegetation and is later evaporated; and depression storage: fraction of the excess precipitation that is stored in surface depressions and is later evaporated, and which never becomes part of runoff or soil moisture.

d)      Define: infiltration: process by which waters enters the soil across the soil surface; infiltration capacity: maximum rate of infiltration under unlimited water supply conditions; and actual infiltration rate: minimum between the supply rate at the surface (e.g., from precipitation) and the infiltration capacity.

e)      Surface runoff starts when the supply rate (i.e., the precipitation rate) exceeds the infiltration capacity rate.

 

Problem 2   The precipitation observation network of a given basin is composed of 4 gauges. The following precipitation amounts were observed at three of the four gauging stations in the watershed for a storm of 10 hours duration.

 

Gauge

Storm Precipitation (in)

Average Annual Precipitation (in)

Gauge Area of Influence (km2)

A

3.15

34.00

9.00

B

4.50

54.00

22.00

C

3.20

37.00

10.00

X

 

40.00

18.00

 

a)                  Using the normal-ratio method obtain an estimate of the precipitation amount for station X.

 

Px = ((40/34)x3.15 in + (40/54)x4.5 in + (40/37)x3.2)/3 in = 3.499 in

 

b)                  Using the Thiessen polygons method determine the mean areal precipitation for the given storm.

 

MAP = (9/59)x3.15 in + (22/59)x4.5 in + (10/59)x3.2 in + (18/59)x3.499 in = 3.768 in

 

c)                  Determine the total volume of water deposited by this storm on this watershed?

 

Volume of Precipitation (P) = MAP x Abasin

 

Volume of Precipitation (P) = (3.768 in)x(0.0254 m/in) x 50x106 m2 = 5647690 m3

Problem 3   A sample of moist air has a temperature of 280 ºK at a pressure of 100,000 Pa, with a mixing ratio of w = 0.01. Compute the following quantities for this air sample: a) dry air density:

Thus, we need the actual vapor pressure of the air, which we can compute from knowledge of the mixing ratio as follows:

so that,

Substituting obtain,

e = 1607.72 Pa; and

rd = (100000 – 1607.72) Pa/287 (J/kg/K)/280 K = 1.22 kg/m3

b) moist air density;

Substituting obtain,

rm = 100000 Pa / 287 (J/kg/K) / 280 K (1 – 0.378 1607.72/100000) = 1.237 kg/m3

c) relative humidity.

Substituting obtain,

es(T=280K) = 611*exp(-2500000(1/280-1/273.15)/461.5) = 992.55 Pa

r.h. = (1607.72 Pa/992.55 Pa)100% = 162%

Problem 4 The initial volumetric moisture content of a soil is 0.2, its volumetric moisture content at saturation is 0.3; and its saturated hydraulic conductivity is Ks = 1.0 cm/h. For these conditions, the capillary suction head at the wetting front, S, is equal to 15 cm. During a rainfall event of constant intensity equal to i = 1.5 cm/h, the cumulative infiltration volume is 3 cm after 2 h.

a)      What is the infiltration capacity at this time?

 

 

            The above equation yields the infiltration capacity as a function of the total accumulated infiltrated volume, which is given for this problem. Thus, substituting obtain,

 

fp(t) = 1.0 cm/h + [(1.0 x 15 x 0.1) cm2/h] / 3 cm = 1.5 cm/h

 

b)      What is the penetration depth of the wetting front at this time?

 

 

Substituting, obtain:

 

                       L = 3 cm / 0.1 = 30 cm

 

c)      For these conditions, when does runoff start?

 

In general, runoff starts when the rainfall intensity exceeds the infiltration capacity. For this problem, the infiltration capacity has decreased to a value of 1.5 cm/h at t = 2 h. If rainfall continues at the same rate, that is at i = 1.5 cm/h, then runoff starts at t = 2 hours.