workshop 2 problem 2

# workshop 2 problem 2 - -1 Problem Lake A round lake of...

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1 Problem. Lake A round lake of diameter d is fed by a river and drained by seepage. The normal flow rate of the river is Q in = 10 4 gal / min and is equal to the rate of seepage. Thus, the water level in the lake is constant. Should the lake level rise, the water from the lake flows through a triangular notch in a retaining wall and into a flood plain. Normally the water level matches the bottom of the triangular notch. !"#\$% ’\$(\$’ )* ’"+\$ ), *-%."’’/ "# #0\$ 1-##-. -2 #0\$ #%)"*34’"% *-#50 )* #0\$ 6".7 8)\$9 -2 6". 2%-. 2’--6 :’")* Suddenly the flow rate of the river increases to 1.5 times the normal rate. The extra water flows out through the triangular notch at a rate determined by the height of the lake above the bottom of the notch. Q notch = αh 5 / 2 (in gal/min) a) What are the units of α if h is measured in meters? Solution. Since Q notch has units gal/min, α must have units of gal min · m 5 / 2 . b) Suppose that the value of α (without respect to units) is 5000. If the flow rate persists indefinitely at 1.5 times the normal rate, to what steady state level,

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