Concept explainers
Find the hydraulic uplift force at the base of the hydraulic structure per meter length.
Answer to Problem 8.5P
The hydraulic uplift force at the base of the hydraulic structure per meter length is
Explanation of Solution
Given information:
The hydraulic conductivity of the permeable soil layer k is
The head difference between the upstream and downstream H is 10 m.
The height of the water level
The depth of permeable layer up to the tip of the hydraulic structure D is 1.67 m.
The depth of permeable layer
Calculation:
Draw the free body diagram of the flow net for the given values as in Figure 1.
Determine the head loss for each drop using the relation.
Here,
Refer Figure 1.
The number of potential drop
Substitute 10 m for H and 12 for
Determine the pressure head at D using the relation.
Here, flow dis is the flow net distance.
Substitute 10 m for H, 3.34 m for
Determine the pressure head at E using the relation.
Substitute 10 m for H, 3.34 m for
Determine the pressure head at F using the relation.
Substitute 10 m for H, 1.67 m for D, 3.5 m for flow dis, and 0.833 for
Determine the pressure head at G using the relation.
Substitute 10 m for H, 1.67 m for D, 8.5 m for flow dis, and 0.833 for
Determine the pressure head at H using the relation.
Substitute 10 m for H, 3.34 m for
Determine the pressure head at I using the relation.
Substitute 10 m for H, 3.34 m for
Determine the hydraulic uplift force at the base of the hydraulic structure per meter length using the relation.
Here,
Take unit weight of water
Substitute
Draw the pressure head diagram as in Figure 2.
Therefore, the hydraulic uplift force at the base of the hydraulic structure per meter length is
Want to see more full solutions like this?
- Given the coefficient k =0.05 m/s and porosity p = 48%, find thetransmissibility (T) in m/s per unit m, if the aquifer width is 1.2 m.Formula: - It is the flow rate per day thru a unit areaunder a unit hydraulic gradient For an aquifer with thickness, Band width, X:T = K*B and Ag = BXThus: Q = (T*X*S)arrow_forwardA hydraulic jump occurs in a horizontal rectangular channel with sequent depths of 0.70 m and 4.2 m. Calculate the rate of flow per unit width, energy loss and the initial Froude number of the flow.arrow_forwardIn fig 3-5, the aquifer thickness is 10 ft, the hydraulic conductivity of the aquifer is 0.06 m/day, and the river water surface is 7m above the bottom of the aquifer. If it is necessary to maintain a water level in the trench not more than 10 m deep, at what rate must water be pumped out of a 100 m long trench? The distance between the edge of the trench and the river is 300 m. Assume all water comes from the river.arrow_forward
- Determine the rate of seepage (in cubic feet/min) under the dam by drawing flow net to scale, and also determine the total uplift force (in psf) acting at the bottom of the dam at Points B and D per unit length of dam. The permeability of the silty sand is 0.2 ft/min. The drawing is to scale. Use scaled drawing (next page) for your flow net sketching and pressure calculations/evaluations. Upstream water level is at El. 94 ft. Downstream water level is at El 68 ft. Dam is 85 ft long and bottom is at el 60 ft. Ground surfaces on both upstream and downstream sides are at El 64 ft.arrow_forwardRefer to Problem 8.4. Using the flow net drawn, calculate the hydraulic uplift force at the base of the hydraulic structure per meter length ( measured along the axis of the structure).arrow_forwardseepage is occurring through the sandy layer underneath the concrete dam.Given: upstream water level = 15.8 m; downstream water level = 2.1 m; thickness of the sandy layer = 1.1 m; coefficient of permeability of the sandy layer = 0.0081 cm/s and L = 48 m. Determine: 1.The seepage flowrate per unit length of the wall in m3/hr/m. 2.Quantity of seepage per day if the dam is 400 m long.arrow_forward
- 11. A channel runs almost parallel to a river as shown in the figure. The water level in the river has an elevation of 36 m. and the elevation of the channel is 33 m. The river and channel are 600 m apart and a previous formation of the average thickness of 9 m and hydraulic conductivity of 0.80 m/hr joints them together. Compute the hydraulic gradient Compute the rate of seepage flow from the river to the channel per meter width in liters per day. If the seepage velocity is 0.048 m/day, compute the void ratio of the previous medium.arrow_forwardAn unconfined aquifer exists where a buried river channel cut into underlying impermeable bedrock. The figure below shows the orientation and pertinent dimensions. The flow rate at the pumping well is 250 gpm, and its radius of influence is 1000 ft. The hydraulic conductivity of the aquifer is 15 ft/d, and the initial saturated thickness is 120 ft. Find the drawdown at the observation well under equilibrium conditions.arrow_forwardFind the conjugate depth of a hydraulic jump in a horizontal channel if the upstream depth is 0.8 m and the velocity of the flow is 8 m/arrow_forward
- A confined aquifer has a thickness of 85 ft. An 86-in diameter well drilled to the bottom of the aquifer, as shown in fig 3-10, if the hydraulic conductivity of the aquifer is 10 ft / day, and if water is originally 170 ft deep in the well, calculate approximately the maximum rate of flow that can be pumped from the well without dewatering any part of the aquifer. Assume 1000 ft reasonable value for the radius of influence. What will be the average velocity ( Darcy velocity ) of flow in the aquifer at a distance 20 ft from the center of the well?arrow_forwardA flow net for flow around a single row of sheet piles in a permeable soil layer is shown in the Figure below. Given that kx= kz = k= 5.5 x 10-3 cm/sec, H1 = 6.5 m and H2 = 2.3 m determine: i. How high (above the ground surface) the water will rise if piezometers are placed at points a and b ii. The total rate of seepage through the permeable layer per unit length iii. The approximate average hydraulic gradient at carrow_forwardAn unconfined aquifer is known to be 32 m thick below the water table. A constant discharge of 2 cubic metres per minute is pumped out of the aquifer through a tubewell till the water level in the tubewell becomes steady. Two observation wells at distances of 15 m and 70 m from the tubewell show falls of 3 m and 0.7 m respectively from their static water levels. Find the permeability in mm/s of the aquifer. a.3.28 x 10^-1 b.4.68 x 10^-1 c.2.58 x 10^-1 d.1.18 x 10^-1arrow_forward
- Principles of Foundation Engineering (MindTap Cou...Civil EngineeringISBN:9781337705028Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage LearningFundamentals of Geotechnical Engineering (MindTap...Civil EngineeringISBN:9781305635180Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage LearningPrinciples of Geotechnical Engineering (MindTap C...Civil EngineeringISBN:9781305970939Author:Braja M. Das, Khaled SobhanPublisher:Cengage Learning