Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft] Ksand=1*10-6 [m/s] Q=10,000 [gal/day] Q z pump 3 [ft] water Find the the depth z, in feet. [pause] In this problem, --- sand

Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft] Ksand=1*10-6 [m/s] Q=10,000 [gal/day] Q z pump 3 [ft] water a 400 foot long trench is shored on both sides, --- sand

Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft] Ksand=1*10-6 [m/s] Q=10,000 [gal/day] Q z pump 3 [ft] water and a pump pumps at 10,000 gallons per day --- sand

Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft] Ksand=1*10-6 [m/s] Q=10,000 [gal/day] Q z pump 3 [ft] water to lower the water surface elevation in the trench by a depth z. sand

Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand flownet L=400 [ft] 5 8 C) 10 D) 12 Ksand=1*10-6 [m/s] Q=10,000 [gal/day] Q z pump 3 [ft] water The water moves through a sand layer with a given hydraulic conductivity and flow net. [pause] sand flownet

Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft] Ksand=1*10-6 [m/s] Q=10,000 [gal/day] Q z pump 3 [ft] water Since this diagram is symmetrical, we’ll only view the left half, for now. sand

Find: z [ft] z Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] Q=10,000 [gal/day] Q z water 3 [ft] [pause] sand

Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q z water 3 [ft] Flow through a flownet is calculated as --- sand

Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q z water 3 [ft] the hydraulic conductivity, --- sand

Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q z water 3 [ft] times the headloss, --- sand

Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q z water 3 [ft] times the number of flow channels divided by the number of drops from the flownet, --- sand

Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q z water 3 [ft] times the length of the structure into and out of the viewing plane. sand

Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q z water 3 [ft] For this problem, --- sand

Find: z [ft] z Q = K * hL * given Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q given z water 3 [ft] we have been given the flowrate, hydraulic conductivity, flownet and length, --- sand

Find: z [ft] z Q = K * hL * given Q hL = K*L Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q given z water Q ND hL = 3 [ft] * K*L NF So we’ll solve for the head loss across the flow net, --- sand

Find: z [ft] z Q = K * hL * given Q hL = K*L Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q given z water Q ND hL = 3 [ft] * K*L NF and the z value we’re trying to find is that headloss. sand

Find: z [ft] z = z Q = K * hL * given Q K*L Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND Q given z water Q ND z = 3 [ft] * K*L NF --- sand

Find: z [ft] z = z = z Q = K * hL * 7.48 given Q K*L K*L Q water L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z water Q ND z = 3 [ft] * K*L NF The flowrate is converted to cubic feet per day, --- 1,337 [ft3/day] ND z = * K*L NF sand

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 the hydraulic conductivity is converted to feet per day, --- m 1,337 [ft3/day] ND z = * 0.283[ft/day]*L NF sand

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 and the length is plugged into the equation without conversion. m 1,337 [ft3/day] ND z = * 0.283[ft/day]*L NF sand

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 From the flownet, we count the number of drops across the soil. m 1,337 [ft3/day] ND z = * 0.283[ft/day]*L NF

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 1 m 1 1,337 [ft3/day] ND z = * 0.283[ft/day]*L NF

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 2 m 1 1,337 [ft3/day] ND z = * 0.283[ft/day]*L NF 2

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 3 m 1 1,337 [ft3/day] ND z = * 0.283[ft/day]*L NF 2 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 4 m 1 1,337 [ft3/day] ND z = * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 5 m 1 1,337 [ft3/day] ND z = 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 6 m 1 6 1,337 [ft3/day] ND z = 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 7 [pause] 7 m 1 6 1,337 [ft3/day] ND z = 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 7 drops 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 Lastly, we count the number of flow channels in the net, and we count, --- 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 1 1 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 1 2 2 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 1 2 3 3 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 4 1 2 3 4 [pause] 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L NF 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 4 1 2 3 4 channels on the left side of the trench, --- 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L 4 2 4 3

Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 4 1 2 3 plus an additional 4 flow channels on the right side of the trench, since we’re only viewing half the flow net. [pause] The headloss across the flow net, 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L 4+4 2 4 3

Find: z [ft] z = z = z = 10.3 [ft] z Q = K * hL * 7.48 given 86,400 Q L=400 [ft] Ksand=1*10-6 [m/s] NF Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 4 1 2 3 our value z, is equal to 10.3 feet. 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L 4+4 2 z = 10.3 [ft] 4 3

Find: z [ft] z = z = z = 10.3 [ft] z 5 Q = K * hL * 8 C) 10 7.48 D) 12 L=400 [ft] Ksand=1*10-6 [m/s] NF 5 8 C) 10 D) 12 Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 4 1 2 3 Looking back at our possible solutions, --- 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L 4+4 2 z = 10.3 [ft] 4 3

Find: z [ft] z = z = z = 10.3 [ft] z AnswerC 5 Q = K * hL * 8 C) 10 L=400 [ft] Ksand=1*10-6 [m/s] NF 5 8 C) 10 D) 12 Q=10,000 [gal/day] Q = K * hL * * L ND gal 7.48 ft3 Q given z s water 86,400 Q ND z = day 3 [ft] * K*L NF ft 3.28 4 1 2 3 The answer is C. 7 m 1 6 1,337 [ft3/day] z = 7 5 * 0.283[ft/day]*L 4+4 2 z = 10.3 [ft] 4 AnswerC 3

? Index σ’v = Σ γ d γT=100 [lb/ft3] +γclay dclay 1 Find: σ’v at d = 30 feet (1+wc)*γw wc+(1/SG) σ’v = Σ γ d d Sand 10 ft γT=100 [lb/ft3] 100 [lb/ft3] 10 [ft] 20 ft Clay = γsand dsand +γclay dclay A W S V [ft3] W [lb] 40 ft text wc = 37% ? Δh 20 [ft] (5 [cm])2 * π/4