Concept explainers
(a)
State whether the statement “pressure head decreases along the flow line” is true or false.
(a)
Answer to Problem 7.1P
The given statement is
Explanation of Solution
Express Bernoulli’s equation as follows:
This equation clearly says that the pressure head is constant along the flow lines.
Thus, the given statement is
(b)
State whether the statement “pressure head is the same along an equipotential line” is true or false.
(b)
Answer to Problem 7.1P
The given statement is
Explanation of Solution
Calculate the total head (h) using the relation.
Here,
From the above equation, it is clear that if there is an increase in the water pressure then it increases depth along the equipotential line. Therefore, pressure is not at the same level along the equipotential line.
Thus, the given statement is
(c)
State whether the statement “flow lines and equipotential lines are not perpendicular to each other in anisotropic soils” is true or false.
(c)
Answer to Problem 7.1P
The given statement is
Explanation of Solution
Express the equation of continuity for two dimensional flow as follows:
The hydraulic conductivity in the horizontal and vertical directions for anisotropic soils is not equal.
The above equation denotes the two families of curves that do not meet at
Thus, the given statement is
(d)
State whether the statement “water level rises to 4.5 m in a standpipe piezometer, the pore water pressure is equal to
(d)
Answer to Problem 7.1P
The given statement is
Explanation of Solution
Calculate the pore water pressure
Here,
Take the unit weight of the water as
Substitute
The pore water pressure at 4.5 m of water level rise is
Thus, the given statement is
(e)
State whether the statement “size of the square flow element is the same at all locations within the flow net” is true or false.
(e)
Answer to Problem 7.1P
The given statement is
Explanation of Solution
While drawing the flow net, the smooth curves are followed by right angle intersection on the intermediate flow lines and equipotential lines.
The curvilinear square grid is the space which is accurately between the pair of flow lines and equipotential lines. Therefore, the size of the square element is varied in the flow net.
Thus, the given statement is
Want to see more full solutions like this?
Chapter 7 Solutions
EBK FUNDAMENTALS OF GEOTECHNICAL ENGINE
- ΔΖ P F D (origin) ΔΧ Figure 1 A: incoming x B: C: incoming y D: outgoing y E: incoming z F: outgoing z x Figure 1 describes a control volume of a saturated confined aquifer where Ax = Ay = Az = 1 m with a porosity of 0.30. 1. For this problem, assume that the fluid and aquifer skeleton are incompressible. Given pore velocities through the control volume depicted in Figure 1: A. 5.00 m/d C. 3.00 m/d E. 2.00 m/d B. ? m/d D. 2.75 m/d F. 1.75 m/d (a) Determine the pore velocity and magnitude of flow Q [L³/T] through face B. (b) Is the fluid moving into or out of the control volume at face B? (c) Which direction is the outgoing fluid moving? This will require two angles to describe the resultant outgoing 3D velocity vector - use to denote the angle of the resultant vector in the x-y plane, and to denote the angle of the resultant vector in the horizontal plane with the vertical plane.arrow_forward4.1 A line load of q = 60kN/m with a = 0 is placed on a ground surface as shown in Figure P4.1. Calculate the increase of pore water pressure at M immediately after application of the load for the cases given below. (a) z = 10m, x = 0m, v=0.5, A=0.45. (b) == 10m, x= 2m, v= 0.45, A=0.6. 2 m 4. G.W.T. Clay XI 1arrow_forward30 cm Water Supply PROBLEM NO. 2 FIGURE A Soil 1 k1 6 cm Soil 2 k2 8 cm Soil 3 Soil 4 k3 2 D k4 2 12 cm Constant-Head Difference 13 cm 7 cm 10 cm -4 cm Datumarrow_forward
- As shown in the figure compute the amount and location of the vertical and horizontal components of the hydrostatic pressure on XY SECTOR GATE L=12M 6.5M I 60° 10M Pv P Y W.S PHarrow_forward7. The figure shows the layers of soil in the tube that is 10 cm by 10 cm in cross section. When the tube is supplied with water, a constant head difference of 30 cm is observed. A B 30 cm с Sample 15 cm 20 cm 25 cm a. Find the equivalent coefficient of permeability. b. Determine the hydraulic gradient. c. Compute the rate of water supply (in cm³/s). K (cm/sec) 2 x 10-³ 3 x 10-³ 4 x 10-³arrow_forwardShow that the hydraulic pressure remains invariant in a horizontal plane parallel to free surface. ļarrow_forward
- Referring to Figure Q3, calculate the following quantities: a. Elevation head, total head, and pressure head at point M on Figure Q3. b. The quantity of water seeping through the dam of Figure Q3 per day. The hydraulic conductivity of the soil is 10-8 Boundary equipotentials Na = 9 N = 3 Boundary flowlines %3D 10 m %3D 12 m 6 m M A (11 m7 m 1 m 2 m Fig. Q3: Earth Damarrow_forwardFor the one-dimensional flow system shown below (units in centimeters):a. What is the value of H needed to have a zero vertical effective stress at point C.?b. What is the value of H needed to have a zero vertical effective stress at point D.?Assume ρsat = 2 Mg /m3 and ρw = 1 Mg /m3. D = 20, L = 16.arrow_forwardA confined aquifer of 15 m constant thickness is sandwiched between two aquicludes as shown in the figure. Piezometer P Piezometer Q Piezometric Surface Aquiclude 34.1 m Aquiclude. L= 2500 m Reference Datum The heads indicated by two piezometers P and Q are 55.2 m and 34.1 m, respectively. The aquifer has a hydraulic conductivity of 80 m/day and its effective porosity is 0.25. If the distance between the piezometers is 2500 m, the time taken by the water to travel through the aquifer from piezometer location P to Q (in days, round off to 1 decimal place) IS_ 55.2 m Aquiferarrow_forward
- 1. A barrel contains 0.2-meter layer of oil floating on water that is 0.4 millimeter deep. If the density of the oil is 600 kg/m^3, find the gage pressure at the oil-water interface. 2. A dam having a triangular section has a vertical face 30m high and base 15m wide. Use SG= 2.4. Determine the height of water that could rise on the vertical side of the dam so that the location of the resultant force is 5 meters from the toe.arrow_forwardA pitot tube having a coefficient of velocity=0.978 is used to measure the velocity of water at the center of a pipe. The stagnation pressure head is 5.67m and the static pressure head in the pipe is 4.73m. What is the velocity in m/s? 5.67 m 4.73 m A O 4.20 O 2.40 O 5.40 O 4.50 基arrow_forwardProblem 8: EGL and HGL (IV) Consider a storage reservoir with a water surface elevation of 270 m. It is connected to a closed conduit (i.e., a pipe) that carries water down to a turbine at elevation 60 m. The friction head loss in the conduit is 20 m. Part A At point D, what are the pressure head P/y, the elevation head z, and the HGL? Part B Copy the diagram below. If the conduit is a closed pipe flowing full, is the velocity head V²/(2g) constant D→E? Answer yes or no, then sketch the EGL above the pipe D-E. Use a solid line. D E z = 270 m T Part C Based on your answer to Part B, sketch the HGL from D-E. Use a dashed line. z = 270 m Part D Now assume the conduit is an open channel. Copy the diagram below. Is the velocity head V²/(2g) constant D→E? Answer yes or no, then sketch the EGL above the pipe D→E. Use a solid line. E D z = 60 m T z = 60 m Part E Based on your answer to Part D, sketch the HGL from D-E. Use a dashed line.arrow_forward
- Fundamentals of Geotechnical Engineering (MindTap...Civil EngineeringISBN:9781305635180Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage Learning