Engineering Hydrology Comprehensive Study Notes

INTRODUCTION

• Hydrology Definition: It is basically an applied science dealing with the occurrence, distribution, and movement of water on the Earth.
• Hydrological Cycle Drivers: The process is driven by the Sun and the Coriolis force.
• Major Components: The cycle consists of six major components: Precipitation ($P$), Infiltration ($I$), Evaporation ($E$), Transpiration ($T$), Surface Runoff ($R$), and Ground water flow ($G$).
• Component Classification:
  • Flow Components: Precipitation, Evaporation, Transpiration, Infiltration, and Runoff.
  • Storage Components: Storage on the land surface (depression storage, ponds, lakes, reservoirs), Soil moisture storage, and Ground water storage.
• Water Budget Equation: For a given catchment in a time interval $\Delta t$, Inflow - Outflow = Change in storage.
  • $(P - R - E - T - G) = \Delta s$
  • Over a long period of time, $\Delta s = 0$.
• Residence Time: Calculated as the volume of water in a phase divided by the average flow rate in that phase.
  • $\text{Residence Time} = \frac{\text{Volume of water in a phase}}{\text{Average flow rate in that phase}}$
  • Residence time of ocean > global ground water.
• Catchment Area: The area of land draining into a stream at a given location. In a closed catchment, water converges to a single point.
• Dew Point: If an air mass (at point A) is cooled to become saturated with water vapor (point D) at constant pressure at that temperature, the resulting temperature is the dew point temperature ($T_D$).

PRECIPITATION

• Saturation Vapour Pressure ($\rho_s$): This occurs when air is fully saturated with vapor. $\rho_s$ increases with an increase in temperature.
• Condensation Requirements: For precipitation to occur, the system requires cooling of air masses, formation of clouds due to condensation, growth of water droplets, and accumulation of moisture.
• Weather Systems of Precipitation:
  • Convective: Caused by the heating of air, leading to rising and adiabatic cooling to form clouds.
  • Orographic: Uplift of an air mass due to a topographic obstruction (mountains).
  • Cyclonic: Lifting of moist air converging into a low-pressure belt.
  • Frontal: Occurs when two air masses of contrasting temperature and density clash.
• Forms of Precipitation:
  • Rain: Water drops between $0.5\,mm$ and $6\,mm$.
    • Light Rain: Trace to $2.5\,mm/h$.
    • Moderate Rain: $2.5$ to $7.5\,mm/h$.
    • Heavy Rain: $> 7.5\,mm/h$.
  • Snowfall: Ice crystals that grow while suspended in the air.
  • Sleet: Small ice pellets ($\text{diameter} \le 5\,mm$).
  • Hail: Spheres of ice with $\text{diameter} > 5\,mm$.
  • Drizzle: Water droplets tiny in size ($< 0.5\,mm$).
  • Glaze: Rain that freezes upon contact with the ground at $0^{\circ}C$.
• Measurement Devices: Known as Pluviometers, Ombrometers, or Hyetometers.
  • Non-recording Gauges: Symons gauge is standard in India. It has a diameter of $12.7\,cm$ and a height of $30.5\,cm$. Measurements are taken daily at 8:30 AM IST (specified in IS : 4986 – 1968).
  • Recording Gauges: Produce a continuous plot of rainfall against time. WMO requires at least 10% of stations to be self-recording.
    • Tipping Bucket: Provides intensity data.
    • Weighing Bucket: Provides a mass curve (accumulated precipitation against time).
    • Natural Siphon Type: Standard in India; float-type gauge that provides a mass curve. The slope of the graph represents rainfall intensity.
• Raingauge Network Standards:
  • In Plains: 1 station per $520\,km^2$.
  • Regions with elevation ~1000m: 1 station per $260$ to $390\,km^2$.
  • Hilly areas with heavy rainfall: 1 station per $130\,km^2$.
• Adequacy and Optimal Number of Gauges ($N$):
  • $\text{Mean precipitation } (P_m) = \frac{\sum P_i}{n}$
  • $\sigma_{n-1} = \sqrt{\frac{\sum (P_i - P_m)^2}{n-1}}$
  • $\text{Coefficient of variation } (C_v) = \frac{100 \times \sigma_{n-1}}{P_m}$
  • $\text{Optimal number of stations } N = (\frac{C_v}{\epsilon})^2$, where $\epsilon$ is the allowable degree of error.
• Estimation of Missing Data:
  • Arithmetic Mean Method: Used if normal precipitation of selected stations is within 10% of the missing station's value ($P_x = \frac{\sum P_i}{n}$).
  • Normal Ratio Method: Used if normal precipitation values do not lie within $(0.9 N_x \text{ to } 1.1 N_x)$.
    • $\frac{P_x}{N_x} = \frac{1}{m} [\frac{P_1}{N_1} + \frac{P_2}{N_2} + ... + \frac{P_m}{N_m}]$
• Data Preparation and Consistency:
  • Normal Precipitation: Average rainfall over 30 years.
  • Average Annual Rainfall: Average rainfall for the last 35 years.
  • Index of Wetness = $(\frac{\text{Actual rainfall}}{\text{Normal rainfall}}) \times 100$.
  • Double Mass Curve Technique: Used to detect inconsistency caused by shifting stations or neighborhood changes. Plot accumulated precipitation of station X ($\sum P_x$) vs. the average of base stations ($\sum P_{av}$). A break in slope indicates inconsistency.
• Areal Average Depth ($P_m$):
  • Arithmetical Mean: Simple average of station values; includes only stations inside the catchment.
  • Thiessen Polygon Method: Includes stations outside; uses area-weighted averages.
    • $P_m = \frac{\sum (P_i \times A_i)}{\sum A_i}$
  • Isohyetal Method: Lines joining points of equal rainfall; most accurate method as it accounts for topography.
    • $P_m = \frac{\sum (A_{ij} \times P_{ij})}{\sum A_{ij}}$, where $P_{ij} = \frac{P_i + P_j}{2}$.
• Frequency and Probability:
  • Plotting Positions: Data arranged in descending order (Rank $M$, Total $N$).
  • Weibull Method: $P = \frac{M}{N+1}$.
  • Return Period ($T$): $T = \frac{1}{P} = \frac{N+1}{M}$.
  • Probable Maximum Precipitation (PMP): The extreme rainfall physically possible for a duration. $PMP = \bar{P} + K \times S$.

ABSTRACTIONS FROM PRECIPITATION

• Evaporation: Rate ($E_L$) depends on vapor pressure, temperature, wind speed, pressure, water quality (1% increase in salinity decreases evaporation by 1%), and water body size.
  • Dalton's Law: $E_L = C(e_s - e_a)$. Evaporation stops when $e_s = e_a$.
  • Meyer's Formula: $E_L = K_m(e_s - e_a)(1 + \frac{u_9}{16})$, where $u_9$ is wind speed at $9\,m$.
• Evaporation Measurement:
  • Evaporimeters: Class-A Pan ($C_p = 0.70$), I.S. Pan ($C_p = 0.80$).
  • Lake Evaporation = $C_p \times \text{Pan Evaporation}$.
• Evapotranspiration (ET):
  • Potential ET (PET): ET when moisture is sufficient to cover needs of vegetation.
  • Actual ET (AET): Real-time ET. If soil is at field capacity, AET = PET.
  • Measurement: Phytometer (transpiration only), Lysimeter (AET), Field plots.
  • Penman’s Equation: Combines energy balance and mass transfer. $PET = \frac{A H_n + \gamma E_a}{A + \gamma}$.
• Infiltration: Water moving downward through the soil surface to recharge aquifers.
  • Infiltration Capacity ($f_c$): Max rate soil can absorb water.
  • Horton’s Equation: $f = f_c + (f_o - f_c) e^{-k_at}$.
  • Infiltration Indices:
    • $\phi$-index: Average rainfall intensity above which volume equals runoff.
    • $W$-index: Average infiltration rate ($W = \frac{P - R - I_L}{t}$).

SURFACE WATER HYDROLOGY (RUNOFF)

• Runoff Coefficient = $\frac{\text{Runoff}}{\text{Rainfall}}$.
• Natural Flow calculation: $R_N = (R_0 - V_r) + V_d + E + E_x + \Delta S$.
• Direct Runoff: Includes surface runoff, prompt interflow, and channel precipitation.
• Base Flow: Delayed flow reaching the stream as groundwater.
• Stream Types:
  • Perennial: Flows year-round; 100% dependable flow > 0.
  • Intermittent: Flows during wet seasons; 100% dependable flow = 0.
  • Ephemeral: Arid zones; no base flow contribution; 100% dependable flow = 0.
• Drought Classifications:
  • Meteorological: PPT deficiency; 26-50% decrease is moderate; >50% is severe.
  • Aridity Index (AI) = $100 \times (\frac{PET - AET}{PET})$.

STREAM FLOW MEASUREMENT

• Stage Measurement: Manual (staff, wire gauges) and Automatic (Float gauge, Bubble gauge).
• Velocity Measurement:
  • Current Meter: $V = a N_s + b$, where $N_s$ is revolutions per second.
  • Depth for Measurement: $V_{avg}$ typically measured at $0.6\,y$ (shallow), or average of $0.2\,y$ and $0.8\,y$ (moderate/deep).
• Discharge Calculation:
  • Slope Area Method: Based on high water marks after a flood. $Q = K \sqrt{S_f}$.
  • Dilution Technique: $Q = Q_1 \frac{C_1 - C_2}{C_2 - C_0}$.
• Rating Curve: Plot of Stage ($G$) vs Discharge ($Q$). A shifting control means the relationship changes over time.

HYDROGRAPHS

• Flood Hydrograph: Plot of Discharge ($Q$) vs Time ($t$). It shows the rising limb, crest segment, and recession (falling) limb.
• Catchment Factors:
  • Form Factor: $\frac{\text{avg. width}}{\text{axial length}}$.
  • Compactness Coefficient: $\frac{\text{Periphery of watershed}}{\text{Circumference of form circle}}$.
• Unit Hydrograph (UH): Direct runoff resulting from $1\,cm$ of effective rainfall (ER). Developed by Sherman.
  • Assumptions: Uniform distribution of ER, constant intensity, time invariance, and linear response (superposition).
• S-Curve: Hydrograph of direct runoff from continuous ER of uniform density (e.g., $1/D\,cm/h$).
• Snyder’s Synthetic UH Parameters:
  • Lag Time ($t_p$): $t_p = C_t (L \times L_{ca})^{0.3}$.
  • Peak Discharge ($Q_p$): $Q_p = \frac{2.78 C_p A}{t_p}$.

FLOODS AND FLOOD FREQUENCY

• Design Flood Types:
  • Standard Project Flood (SPF): Severe combination of metrological conditions (~80% of PMF).
  • Probable Maximum Flood (PMF): Extreme rare catastrophic floods.
• Estimation Methods:
  • Rational Method: $Q_p = \frac{1}{36} C i A$ (for catchments up to $50\,km^2$).
  • Dickens Formula: $Q_p = C_D (A)^{3/4}$.
  • Ryves Formula: $Q_p = C_R (A)^{2/3}$.
  • Inglis Formula: $Q_p = \frac{124 A}{\sqrt{A + 10.4}}$.
• Gumbel’s Method: $X_T = \bar{X} + K \sigma_{n-1}$, where $K$ is the frequency factor.

FLOOD ROUTING

• Continuity Equation: $I - Q = \frac{dS}{dt}$.
• Reservoir Routing: Storage is a function of elevation/outflow only. Includes Modified Pul’s and Goodrich methods.
• Channel Routing (Muskingum Method):
  • Storage ($S$): $S = K[x I^m + (1 - x) Q^m]$.
  • Outflow Equation: $Q_2 = C_0 I_2 + C_1 I_1 + C_2 Q_1$.
  • Coefficients: $C_0 + C_1 + C_2 = 1$.
• Trap Efficiency: $\frac{\text{Sediments retained}}{\text{Total sediments}} \times 100$.

GROUND WATER

• Porosity ($\eta$): Sum of Specific Yield ($S_y$) and Specific Retention ($S_r$).
  • Specific Yield ($S_y$): Water extracted by gravity. ($\text{Clay} < \text{Sand} < \text{Gravel}$).
  • Specific Retention ($S_r$): Fraction held back ($\text{Clay} > \text{Sand} > \text{Gravel}$).
• Storage Coefficient ($S$): Volume of water released per unit plan area per unit fall in piezometric head.
• Steady Flow Equations:
  • Thiem's (Confined): $Q = \frac{2 \pi K B (h_2 - h_1)}{2.303 \log(\frac{r_2}{r_1})}$.
  • Dupuit's (Unconfined): $Q = \frac{\pi K (h_2^2 - h_1^2)}{2.303 \log(\frac{r_2}{r_1})}$.
• Radius of Influence: $R = 3000 s \sqrt{K}$.

MEASUREMENT INSTRUMENTS AND TERMINOLOGY

• Instruments:
  • Phytometer: Transpiration.
  • Anemometer: Wind speed.
  • Hygrometer: Humidity.
  • Psychrometer: Relative humidity.
  • Atmometer: Evaporation.
• Isopleths (Equal value lines):
  • Isohyet: Rainfall.
  • Isotherm: Temperature.
  • Isobar: Pressure.
  • Isochrone: Travel time.
  • Isohaline: Salinity.
  • Isohel: Sunshine.
  • Isonif: Snowfall.