please answer these questions and show your work 2. Several years ago, a state h

Question

please answer these questions and show your work

2. Several years ago, a state highway department built a highway across a shallow lake by placing the clayey fill shown in Figure 2. The top of this fill is above the high water level, thus protecting the highway from flooding. It is now necessary to install a buried pipeline beneath the roadway. To install this pipe, the contractor plans to make a temporary excavation using steel sheet piles as shown in Figure 2. The contractor plans to use sump pumps at 50 ft intervals to maintain the water level at the bottom of excavation. Once the pipe has been installed, the excavation will be backfilled and the pumps and sheet piles removed. Using the flow net provided in Figure 2, you are asked to perform the following tasks in connection with this project: [6 pointsl (a) Determine the hydraulic gradient right below the bottom of the excavation between the two sheet pile walls. [3 point] (b) Compute the minimum required capacity for each pump, expressed in gallons per minute. (3 points]

Explanation / Answer

Hydraulic gradient i = change in head / length of corvelener squire

total heal drop = 16

head loss= 32.7 -21.5 =11.2 ft

head loss per drop = 11.2/16 = 0.7 ft

length of corvelener squire just below excavation = 5/4 = 1.25 ft

Hydraulic gradient i = 0.7/1.25=0.56

flow q= kh Nf/Nd

Nf= 4 Nd = 16

k= 5*10-2 cm /sec = 9.842 *10-2 ft/min ( 1 cm /sec = 1.9685 ft/min)

q= 9.842 *10-2*11.2*4/16

q= 0.275576 ft3/min/ft length

Q= q*L

Given L pipe distance = 50 ft

Q= 50* 0.275576 = 13.7788 ft3/min = 103.0726 gal /min

Q= pump capacity

thanks

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