Question

Note k values are in cm/s need to be changed to in/s

Draw the piezometric line, compute the hydraulic gradient, and compute the flowrate through the seepage apparatus shown below: 10" scale 10 (k- 10 cm/s) 1 12"* 12" Headwater 10" Tailwater Head Profile

Answer 1

Areas A_1 = 8 times 4 = 32 ix^2 A_2 = 8 times 8 = 64 in^2 let v_1 rightarrow velocity in narrow pipe v_2 rightarrow velocity in Broad pipe By law v_1 = k Delta h_1/L_1 v_1 = 10^-4/2.54 times Delta h_1/12 v_1 = 3.28 times 10^-6 Delta h_1 im/s - ()1) \r\n v_2 = k i_2 v_2 = 10^-4/2.54 times Delta h_2/12 v_2 = 3.28 times 10^-6 Delta h_2 in/s - (2) since Discharge has to be same Rightarrow Q = A_1 v_1 = A_2 v_2 (or) v_1 = Q/A_1 and v_2 = Q/A_2 from adding (1) and (2) v_1 + v_2 = 3.28 times 10^-6 (Delta h_1 + Delta h_2) Q/A_1 + Q/A_2 = 3.28 times 10^-5 Rightarrow Q)1/32 + 1/64) = 3.28 times 10^-5 \r\n Rightarrow Q 7 times 106-4 in^3/s Hydraulic gradient = Delta h/L = 10/24 = 0.416 complete Delta h_1 and Delta h_2 v_1 = 7 times 10^-4/32 = 2.18 times 10^05 in/s