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\rhead{FALL 2024}
\lfoot{CE 3354 Engineering Hydrology }
\cfoot{EXAM 1}
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\begin{centering}
\textbf{CE 3354 Engineering Hydrology} \\
\textbf{Exam 1, Fall 2024}\\
\end{centering}
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Students should write their name on \textbf{all sheets of paper}.  \newline 
Students are permitted to use the internet to help answer questions.  \newline 
Students are permitted to use their own notes and the textbook.\newline 
Students are \textbf{forbidden} to \textbf{communicate with other people} during the examination.
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\begin{enumerate}
%%%%%% MULTIPLE GUESS PORTION %%%%%%%%%%%%%%%%%%%%
\item Hydrology is
\begin{enumerate}[a)]
\item Study of the atmosphere, ocean, and surface waters
\item The study of the occurrence, distribution, and movement of water above, on, and below the surface of the earth
\item A study of the processes of evaporation, infiltration, and storage
\item The study of the relationship between rainfall and runoff
\end{enumerate}
\item The fundamental unit of hydrology is ?
\begin{enumerate}[a)]
\item The rainfall depth
\item The main channel length
\item The main channel slope
\item The watershed 
\end{enumerate}
\item What is the relationship between the Annual Exceedance Probability (AEP) and the Annual Recurrence Interval (ARI)?
\begin{enumerate}[a)]
\item	The ARI is the average number of years between years containing one or more events exceeding a prescribed magnitude
\item	The AEP and ARI are the multiplicative inverse of one another
\item	The AEP is a plot of probability and magnitude
\item	The ARI is a plot of probability and magnitude
\end{enumerate}

\item An annual recurrence interval of 100-years is equivalent to an AEP of what percent?
\begin{enumerate}[a)]
\item 1-percent.
\item 10-percent.
\item 50-percent.
\item 100-percent.
\end{enumerate}
\item What is a flood frequency curve?
\begin{enumerate}[a)]
\item A plot of the discharge magnitude and the Weibull plotting position
\item A plot of the frequency and discharge
\item A plot of estimated exceedance probability and discharge
\item A plot of discharge and time
\end{enumerate}
\item What is a plotting position?
\begin{enumerate}[a)]
\item Location in a chart of a data pair
\item The multiplicative inverse of relative frequency
\item An estimate of probability associated with an observation based on its position within a ranked sample set
\item An estimate of probability associated with an observation based on its magnitude relative to the arithmetic mean
\end{enumerate}
\item To what type of data series would we apply the Bulletin 17C procedure ?
\begin{enumerate}[a)]
\item Annual maximum rainfall
\item Hourly rainfall
\item Annual maximum discharge
\item Instantaneous discharge
\end{enumerate}
\item Rainfall behavior is expressed as a combination of 
\begin{enumerate}[a)]
\item depth and duration
\item intensity and probability or frequency
\item duration and probability or frequency
\item depth or intensity, duration, and probability or frequency
\end{enumerate}
\item Rainfall intensity is 
\begin{enumerate}[a)]
\item the ratio of accumulated depth to duration
\item instantaneous rainfall rate
\item slope of the depth duration curve at a duration of one hour
\item integral of the depth duration curve from 0 to 24 hours
\end{enumerate}

\newpage
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\item Figure \ref{fig:ddf-curve.jpg} is a depth-duration-frequency plot for precipitation.

\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=6in]{ddf-curve.jpg} 
   \caption{Depth-duration-frequency curve}
   \label{fig:ddf-curve.jpg}
\end{figure}

The approximate depth, in millimeters, for a 4 hour, 100-yr (1\% chance) storm is 
\begin{enumerate}[a)]
\item 125 millimeters
\item 75 millimeters
\item 55 millimeters
\item 45 millimeters
\end{enumerate}
\clearpage



\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=6in]{flood-frequency-curve.jpg} 
   \caption{Flood frequency curve for a gaging station}
   \label{fig:flood-frequency-curve.jpg}
\end{figure}

\item Figure \ref{fig:flood-frequency-curve.jpg} is a flood frequency curve.   The probability of observing a discharge of magnitude of $50,000~CFS$ or more is
\begin{enumerate}[(a)]
\item $0.01$
\item $0.05$
\item $0.10$
\item $0.50$
\end{enumerate}

\item The median discharge from Figure \ref{fig:flood-frequency-curve.jpg} is
\begin{enumerate}[(a)]
\item $10,000~CFS$
\item $20,000~CFS$
\item $50,000~CFS$
\item $90,000~CFS$
\end{enumerate}

\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%% From ES1-P4 %%%%%%%%%%%%%%%%%%%%%%%%%%
\item The equation $k\frac{dQ}{dt} + Q(t) = I(t)$ is used to describe the response of streamflow to a constant rate of precipitation applied indefinitely on some watershed.  
Suppose that $Q(t)=0$ for $t=0$, the watershed characteristic time constant is $k=2~hrs$, and $I(t) =2$ for $t=[0,12)~hrs$ and then $I(t) =0$ for $t=[12,24]~hrs$. 

Determine:
\begin{enumerate}
\item The necessary equation(s) to predict the response $Q(t)$ over the 24-hour period.
\item Plot the values of $Q(t)$ over the 24-hour period (i.e. complete Figure \ref{fig:hydrograph} below, showing the discharge $Q(t)$).
\end{enumerate}

\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=6.0in]{HydrographPlot001.png} 
   \caption{Plot of Runoff for Watershed described by $k\frac{dQ}{dt} + Q(t) = I(t)$, where $I(t)$ is as shown (in blue)}
   \label{fig:hydrograph}
\end{figure}
Show your work below (and on next page)
\clearpage
Continued
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%%%%%%%%%%%%%%%%%%%%% From ES-2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  Figure \ref{fig:topoMap.jpg} is a  topographic map of a small drainage basin.  The contours show elevation in meters.  Many of the contours are labeled.   A culvert structure is located on the Eastern portion of the basin, near the outlet shown on Figure \ref{fig:topoMap.jpg}.   The red line is a proposed impoundment alignment, beneath which the culvert structure is placed.  

\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=6.5in]{image_with_grid.png} 
   \caption{Topographic Map of a portion of the Earth.  Elevations are in $meters$.  Each square is $150~meters$ on a side. North (by convention) is up.}
   \label{fig:topoMap.jpg}
\end{figure}

\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=6in]{Pan1.JPG} 
   \caption{Multiple-barrel outlet structure}
   \label{fig:Pan1.JPG}
\end{figure}

Figure \ref{fig:Pan1.JPG} is a photograph of a representative culvert system comprised of 4-parallel , 4-foot diameter, 100-foot long culverts.  The lowest portion of the proposed impoundment structure directly above the culverts is at elevation 810 meters.  The culverts are to be laid on a dimensionless slope of $0.02$.

\begin{enumerate}[a)]
\item Delineate the drainage area to the culverts using the 810 meter elevation as the pour point elevation (located at the blue marker in the drawing).
\item Determine the area of each small square.
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\item Estimate the drainage area in square meters of the drainage basin.  
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\item Convert the drainage area from square meters into acres.   
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\item Convert the drainage area from acres into square miles.   
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\item The water surface area when the culvert system (like a dam, with 4 holes in the wall) impounds water to a water surface elevation of $760~meters$ is essentially zero.  Complete the elevation (side) view sketch of the embankment and culvert system in Figure \ref{fig:CulvertSystemElevation} by indicating the elevations on the sketch of the roadway crest, the culvert inlet elevation (also the upstream base of the embankment), and culvert outlet elevation.
\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[height=2.6in]{CulvertSystemElevation.jpg} 
   \caption{Culvert system elevation view sketch}
   \label{fig:CulvertSystemElevation}
\end{figure}
\clearpage

\item Estimate the water surface area (area of the pool on the upstream side of the embankment) when the embankment impounds water to a water surface elevation of $780~meters$.  Describe how you made the estimate.
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\item Estimate the water surface area when the embankment impounds water to a water surface elevation of $790~meters$.  Describe how you made the estimate.
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\item Estimate the water surface area when the embankment impounds water to a water surface elevation of $810~meters$.  Describe how you made the estimate.
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\end{enumerate}
\clearpage

\item Figure~\ref{fig:RARO-DATA.pdf} is a tabulation of an observed storm and runoff for the drainage area depicted by the map in Figure~\ref{fig:topoMap.jpg}.  The runoff was measured before the installation of the roadway, at the location indicated by the blue circle on the map.


\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=2.5in]{RARO-DATA.pdf} 
   \caption{Cumulative rainfall for a 24-hour period on watershed determined for Figure \ref{fig:topoMap.jpg}}
   \label{fig:RARO-DATA.pdf}
\end{figure}
\clearpage
\begin{enumerate}[a)]
\item  Estimate the total \textbf{volume} of runoff in cubic feet from the storm.  Describe how you made your estimate.
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\item Convert the estimate of runoff volume from cubic feet into watershed inches.
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\item How long (in hours) from the beginning of rainfall until the peak discharge occurs?
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\item What is the fraction of rainfall that becomes runoff?
\end{enumerate}
\clearpage

\end{enumerate}
\end{document}
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\item How can one calculate the Annual Exceedance Probability (AEP) from the Annual Return Interval (ARI)?
\begin{enumerate}[a)]
\item	Cannot
\item	$AEP = \frac{1~yr}{ARI}$
\item	$ARI = \frac{1~yr}{AEP}$
\item	$ARI = \frac{Rank_i}{N+1}$
\end{enumerate}

%\item In the rational equation, $Q = CIA$, 
%\begin{enumerate}[a)]
%\item the intensity, $I$, is the ratio of depth to the time of concentration
%\item the intensity, $I$, is the ratio of depth to watershed area
%\item the intensity, $I$, is the ratio of depth to watershed discharge
%\item the intensity, $I$, is the ratio of depth to watershed impervious cover
%\end{enumerate}
%\item Regional analysis is used to
%\begin{enumerate}[a)]
%\item delineate watersheds
%\item relate discharge to drainage area
%\item construct regression equations from historical data on many streams within a region
%\item establish a typical functional drainage area
%\end{enumerate}

\item  The watershed in Figure \ref{fig:topoMap.jpg} is located in Briscoe County, Texas. Figure \ref{fig:countymap.pdf} is a map of
counties in Texas. Figures  \ref{fig:DDF-Atlas-5yr} and \ref{fig:DDF-Atlas-10yr} are excerpts from the Texas DDF Atlas.
\begin{enumerate}[a)]
\item Circle Briscoe county on Figure \ref{fig:countymap.pdf}.
\item Circle Briscoe county on Figure \ref{fig:DDF-Atlas-5yr}.
\item Circle Briscoe county on Figure \ref{fig:DDF-Atlas-10yr}.
\item Write the formula that converts the Annual Exceedence Probability (AEP) into an Annual Recurrence Interval (ARI).
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\item Estimate the precipitation depth in Brown county for a 2 hour storm with an Annual Exceedence Probability (AEP) of 0.2 (20 \%).
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\item Estimate the average rainfall intensity in Brown county for a 2 hour storm with an Annual Exceedence Probability (AEP) of 0.1 (10 \%).
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\end{enumerate}

\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=6in]{countymap.jpg} 
   \caption{Cumulative rainfall for a 24-hour period on watershed determined for Figure \ref{fig:topoMap.jpg}}
   \label{fig:countymap.pdf}
\end{figure}

\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=6in]{DDF-Atlas-5yr.jpg} 
   \caption{Cumulative rainfall for a 24-hour period on watershed determined for Figure \ref{fig:topoMap.jpg}}
   \label{fig:DDF-Atlas-5yr}
\end{figure}

\begin{figure}[h!] %  figure placement: here, top, bottom, or page
   \centering
   \includegraphics[width=6in]{DDF-Atlas-10yr.jpg} 
   \caption{Cumulative rainfall for a 24-hour period on watershed determined for Figure \ref{fig:topoMap.jpg}}
   \label{fig:DDF-Atlas-10yr}
\end{figure}

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