King Fahd University of Petroleum & Minerals Civil Engineering Dept. CE 331 Engineering Hydrology HW NO. 6 Spring 07-08 Instructor: Rashid .I. Allayla Student Name: ________________________ Student No. ___________________________ SCORE: ____________________ Problem 1: A silty sand sample have the following properties: Total mass = 1523.6 g Mass of oven dried sample: 1318.3 g Total volume of sample: 728.2 cm3 Density of the solid: 2.7 g/cm3 Calculate: a) Porosity b) Volumetric Water Content c) Dry bulk density Problem 2: The following field data was taken from piezometers installed side by side at a single site (each 100 m apart): Piezometer: Elevation at surface (m) Depth of Piezometer (m) Depth to water (m) A 450 150 27 B 450 100 47 C 450 50 36 If A, B and C (m) refer to the points of measurement of piezometers a, b and c. Calculate: a) b) c) d) The hydraulic head at A, B and C (m) The pressure head at A, B and C (m) The elevation head at A, B and C (m) The hydraulic gradient between A and B and B and C. A B 450 100 m C 100 m 423 414 403 400 350 300 Datum a) Hydraulic head @ A = 423 - 300 = 123 m B = 50 + (403-350) = 103 m C = 100 + (414-400) = 114 m b) Pressure head @ A: 423 – 300 = 123 m B: 403 – 350 = 53 m C: 414 – 400 = 14 m d) Elevation heads: A= 0, B= 50 m and C= 100 m e) Gradient A to B = (123-103) / 100 = 0.2 f) Gradient B to C = (103-114) / 100 = -0.11 Problem 3: A soil sample is tested in laboratory. The column has an inside diameter of 10 cm and the length of the soil sample is 25 cm. With steady flow of Q = 1.7 cm 3 / min, the head difference between the two manometers is 15 cm. Calculate: a) The hydraulic conductivity of the sample. b) The intrinsic permeability k if the water temperature is 30O C Q = - K A (h2-H1) / L K = - Q L / A ∆H = - (1.7) (25) / [(π)(52) (-15) = 0.036 cm/min