Hydrology and Floodplain Analysis by Bedient et.al. Chapter 1 Problem 7


Problem:

Clear Lake has a surface area of 708,000 m2 (70.8 ha.). For a given month, the lake has an inflow of 1.5 m3/s and an outflow of 1.25 m3/s. A +1.0-m storage change or increase in lake level was recorded. If a precipitation gage recorded a total of 24 cm for this month, determine the evaporation loss (in cm) for the lake. Assume that seepage loss is negligible.


Solution:

We are given the following values:

\begin{align*}
\text{Area}, \ A&=708,000 \ \text{m}^2 \\
\text{Inflow}, \ I&=1.5 \ \text{m}^3/\text{s} \\
\text{Outflow}, \ O & = 1.25 \ \text{m}^3/\text{s} \\
\text{change in storage}, \ \Delta S & = 1.0 \ \text{m} \\
\text{Precipitation}, \ P&=24 \ \text{cm} \\
\text{time}, \ t &= 1 \ \text{month} = 30 \ \text{days}
\end{align*}

The required value is the \text{Evaporation}, \ E.

We shall use the formula

\Delta S=I+P-O-E

Solving for E in terms of the other variables, we have

E=I+P-O-\Delta S

Before we can substitute all the given values, we need to convert everything to the same unit of cm.

\begin{align*}
\text{Inflow}&=\frac{1.5\:\frac{\text{m}^3}{\text{s}}\cdot \frac{100\:\text{cm}}{1\:\text{m}}\cdot \frac{3600\:\text{s}}{1\:\text{hr}}\cdot \frac{24\:\text{hr}}{1\:\text{day}}\cdot \frac{30\:\text{days}}{1\:\text{month}}\cdot 1\:\text{month}}{708,000\:\text{m}^2} \\
\text{Inflow}&=549.1525 \ \text{cm}
\end{align*}
\begin{align*}
\text{Outflow}&=\frac{1.25\:\frac{\text{m}^3}{\text{s}}\cdot \frac{100\:\text{cm}}{1\:\text{m}}\cdot \frac{3600\:\text{s}}{1\:\text{hr}}\cdot \frac{24\:\text{hr}}{1\:\text{day}}\cdot \frac{30\:\text{days}}{1\:\text{month}}\cdot 1\:\text{month}}{708,000\:\text{m}^2} \\
\text{Outflow}&=457.6271 \ \text{cm}
\end{align*}
\Delta S=1.0 \ \text{m} \times \frac{100 \ \text{cm}}{1.0 \ \text{m}}=100 \ \text{cm}

Now, we can substitute the given values in the formula

\begin{align*}
E & =I+P-O-\Delta S \\
E& =549.1525 \ \text{cm}+24 \text{cm}-457.6271 \ \text{cm}-100 \ \text{cm} \\
E& =15.5254 \ \text{cm} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}

Hydrology and Floodplain Analysis 5th Edition by Bedient et. al. Chapter 1 Problems

Problem 1Problem 2Problem 3Problem 4Problem 5
Problem 6Problem 7Problem 8Problem 9Problem 10
Problem 11Problem 12Problem 13Problem 14Problem 15
Problem 16Problem 17Problem 18Problem 19Problem 20
Problem 21Problem 22Problem 23Problem 24Problem 25
Problem 26Problem 27Problem 28Problem 29Problem 30
Hydrology and Floodplain Analysis Solution Manual

Hydrology and Floodplain Analysis 5th Edition by Bedient, Huber and Vieux

Chapter 1: Hydrologic Principles

Chapter 2: Hydrologic Analysis

Chapter 3: Frequency Analysis

Chapter 4: Flood Routing

Chapter 5: Hydrologic Simulation Models

Chapter 6: Urban Hydrology

Chapter 7: Floodplain Hydraulics

Chapter 8: Ground Water Hydrology

Chapter 9: Design Applications in Hydrology

Chapter 10: GIS Applications in Hydrology

Chapter 11: Radar Rainfall Applications in Hydrology

Chapter 12: Severe Storm Impacts and Flood Management

Chapter 9: Design Applications in Hydrology

Chapter 10: GIS Applications in Hydrology

Chapter 11: Radar Rainfall Applications in Hydrology

Chapter 12: Severe Storm Impacts and Flood Management

Chapter 13: Case Studies in Hydrologic Engineering: Water Resource Project