Figure $1$ Hydrograph determined from flow measurements on a spring

$(30$ points$)$ The volumetric discharge of a river at the start of a base flow recession was $740$

$\frac{m^3}{sec}$; after $60$ days, the volumetric discharge declined to $510\frac{m^3}{sec}.$

a$)$ What is the recession constant k $?$

b$)$ What would be the base flow after $100$ days?

c$)$ What is the total volume of base flow discharge after $100$ days?

d$)$ What is the potential volume of base flow?

e$)$ What is the residual volume of base flow after $100$ days? $($The residual volume of

base flow is the difference between the potential volume of base flow and the actual volume

of base flow over a given period, which is $100$ days for this problem$).$

$(20$ points$)$ An aqueduct has smooth earthen sides and bottom. The slope of the water

surface is $1\mathrm{.}5f\frac{t}{m}$ile. The channel is trapezoidal with a $45$ degrees angle to the sides of the

trapezoid and a bottom segment that is $8\mathrm{.}8$ ft wide $($the width at the top of the trapezoidal is

larger than the width at the base of the trapezoidal$).$ The water in the aqueduct is $3\mathrm{.}7$ ft deep

in the center. The Manning roughness coefficient is $0\mathrm{.}012.$ A$)$ What is the hydraulic radius? B$)$

What is the average velocity of water in the aqueduct? C$)$ What is the volume of flow in the

aqueduct?

$(15$ points$)$ Explain A$)$ What is total porosity and effective porosity. B$)$ Why does clay

have such a different total porosity from the effective porosity, but well$-$sorted sand may have

a much smaller difference between its total porosity and effective porosity?