Chapter 6: Problems

  1. Consider a region of flow such as ABCDEA in Figure 6.1. Set BC = 1000 m and make the length of CD equal to twice the length of AB. Draw flow nets for the following homogeneous, isotropic cases:
    1. AB = 500 m, AD a straight line.
    2. AB = 500 m, AD a parabola.
    3. AB = 100 m, AD a straight line.
    4. AB = 200 m, AE and ED straight lines with the slope of AE twice that of ED.
    5. AB = 200 m, AE and AD straight lines with the slope of ED twice that of AE.
    1. Label the recharge and discharge areas for the flow nets in Problem 1 and prepare a recharge-discharge profile for each.
    2. Calculate the volumetric rates of flow through the system (per meter of section perpendicular to the flow net) for cases in which K = 10–8, 10–6, and 10–4 m/s.
  1. Assume a realistic range of values for P and E in Eqs. (6.2) through (6.6) and assess the reasonableness of the values calculated in Problem 2(b) as components of a hydrologic budget in a small watershed.
  1. What would be the qualitative effect on the position of the hinge line, the recharge-discharge profile, and the baseflow component of runoff if the following geological adaptations were made to the system described in Problem 1(d)?
    1. A high-permeability layer is introduced at depth.
    2. A low-permeability layer is introduced at depth.
    3. A high-permeability lense underlies the valley.
    4. The region consists of a sequence of thin horizontally bedded aquifers and aquitards.
  1. On the basis of the flow-net information in this chapter, how would you explain the occurrence of hot springs?
  1. Label the areas on the flow nets constructed in Problem 1 where wells would produce flowing artesian conditions.
  1. A research team of hydrogeologists is attempting to understand the role of a series of ponds and bogs on the regional hydrologic water balance. The long-term objective is to determine which of the surface-water bodies are permanent and which may diminish significantly in the event of a long-term drought. The immediate objective is to assess which surface-water bodies are points of recharge and which are points of discharge, and to make calculations of the monthly and annual gains or losses to the groundwater system. Outline a field measurement program that would satisfy the immediate objectives at one pond.
  1. On the flow net drawn in Problem 1(b), sketch in a series of water-table positions representing a water-table decline in the range 5- to 10-m/month (i.e., point A remains fixed, point D drops at this rate). For K = 10–8, 10–6, and 10–4 m/s, prepare a baseflow hydrograph for a stream flowing perpendicular to the diagram at point A. Assume that all groundwater discharging from the system becomes baseflow.
    1. Prove that a decrease in atmospheric pressure creates rising water levels in wells tapping a confined aquifer.
    2. Calculate the water-level fluctuation (in meters) that will result from a drop in atmospheric pressure of 5.0 × 103 Pa in a well tapping a confined aquifer with barometric efficiency of 0.50.