3.1 Derive the appropriate shallow water equationsfor a single moving layer of fluid of density p1 abovea rigid floor, and where above the moving fluid is astationary fluid of density Po, where po < P1. Showthat as (Po/p1) → 0 the usual shallow water equa-tions emerge.

Draw the figure The vertical momentum equation is just the hydrostatic equation, ∂P∂z=-ρog…

Derive the appropriate shallow water eq For a single moving layer of fluid of densit a rigid floor, and where above the moving stationary fluid of density po, where Po < F hat as (o0/o1) → 0 the usual shallow wate

Derive the appropriate shallow water eq For a single moving layer of fluid of densit a rigid floor, and where above the moving stationary fluid of density po, where Po < F hat as (o0/o1) → 0 the usual shallow wate

Fundamentals of Geotechnical Engineering (MindTap Course List)

5th Edition

ISBN:9781305635180

Author:Braja M. Das, Nagaratnam Sivakugan

Publisher:Braja M. Das, Nagaratnam Sivakugan

Chapter7: Seepage

Section: Chapter Questions

Problem 7.1P

See similar textbooks

Related questions

Q: نقطة واحدة In fig. if h1= 0.5 m, h2= 1.5 m and the fluid y2 S.G= 13.6, ylis water, what ?is the…

Q: SITUATION 2. A triangular tank facing downward has unit weight equal to 27 kN/m3 and weighs 0.6 kN.…

Q: A 50 mm diameter circular sharp-edged orifice at the side of a tank discharges water under a head of…

A: Given: The diameter of the orifice is 50 mm. The head is 3 m. The coefficient of contraction Cc is…

Q: For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through a pipe of radius…

A: Given data- fully developed laminar flow-dynamic viscosity μ=0.001 Pa-sradius of pipe R=5 cm=0.05…

Q: SG 0.90 2) difference, Ah, between the water levels in the two open tanks shown in the figure.…

Q: The Steam has the following data: Average stream cross-section = 38.35 sq.m. Wetted perimeter =…

A: Discharge is defined as the volume of fluid collected per unit time period. The discharge is equal…

Q: 2. A pipe carries water at a flow rate of 90 L/s. Determine the minimum inside diameter so that the…

A: Given :- Flow rate of the water (Q) = 90 L/s Also, 1000 L/s = 1 m3/s So, Flow rate of the water (Q)…

Q: Water flow in a pipe of diameter 600mm having a length of 2200 m at a velocity of 2m/s. At the end…

Q: For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through a pipe of radius…

A: Given data- dynamic viscosity μ=0.001 Pa-sRadius R=5 cmpressure gradient ∂P∂x=-10 Pa/mradial…

Q: which of the following mostly depends on headloss? a. pressure head b. elevation head c. velocity…

A: Given data in question Headloss Uniform sized pipe Compressible fluid To be discussed Which is the…

Q: The tapered settling tank is completely filled with oil. Determine the resultant force the oil…

A: The trapezoidal channel is useful in storing water and creating a maximum flow of water use when…

Q: 23. The ratio of the momentum correction factor to the energy correction factor for a laminar flow…

A: given- Laminar flowpipe flow

Q: 2) Assuming we have a fluid with SG-0.6, and height of fluid in the piezometer tube equal to h=10m,…

A: To Determine Pressure at point M, P & S

Q: Oil (s=0.80) and viscosity (u = 0.098 Pa – sec) flow from a reservoir of surface elevation 100…

A: Please find attached images for solution

Q: The pressure-flow characteristic of a pump can be expressed in equation form as AP, = Qo - aQ? The…

A: Pressure: It is defined as the amount of force that is applied normally to the surface which is a…

Q: Q1) Using a system similar to that shown in figure, if air pressure p = 50 kPa., and the depth h1 =…

A: To Determine Flow rate in nozzle, Q Height h2

Q: The water conveyed by a circular cross section pipe flows through the full section. The diameter of…

A: Reynold's Number is defined as the ratio of inertia force to viscous force. V – Velocity of flow…

Q: SITUATION. A closed cylindrical tank with 0.60 m diameter and 1.0 m height is fully-filled with…

Q: Water of temperature 30° is flowing with flow rate 0.055 liters/s in a straight 50mm diameter UPVC…

Q: Problem 6 For the tank shown below (width = 1.25 m), determine (6.a) the maximum horizontal…

Q: Consider an irrotational region of flow composed of a line source of strength V. /L at location (−a,…

A: The figure is shown below,

Q: Compute for the flow rate in cubic meter per second of oil with p = 950 kg/m³ and v = 0.00002 m?/s,…

Q: A reservoir contains water has a vertical circular orifice 25.2mm diameter and is first plugged up…

A: Given : H = 2.785m QL = 141 lt/min = 2.35 × 10-3 m3/sec Cc, Cv, and Cd are the hydraulic…

Q: A pipe has a length of 447 meters. Water is flowing in the pipe at a rate of 0.53 m3/s. If the…

Q: Q 3: Q: During the suction, the siphon tube will run continuously as long as reservoir fluid is…

A: Assuming that the flow is ideal. Using bernoullis equation at free surface(1) and pipe exit(2).the…

Q: Air flows steadily along a streamline from point (1) to point (2) with negligible viscous effects.…

A: condition At point 2: at point 2 velocity of floe is zero so point 2 is situated in a large area…

Q: Task 1: A dam is used to store water, and a circular gate which is hinged at its bottom edge is used…

Q: Consider the system below with PA=50 kPa, VA=5 m/s and d=20 cm. Determine the Problem 3.2.2 heights…

A: Given information:

Q: -8.33 -0.12 8.33 (1) 0.12 -L Darcy Experiment A set-up of Darcy Experiment involves measuring the…

A: Given data Hydraulic head at section-1 (h1) = 66cm Hydraulic head at section-2 (h2) = 54cm Length…

Q: A conical tube of length 2m is fixed vertically with smaller end upward. Velocity of flow at smaller…

Q: The figure shows a cylinder of 4 m dlameter in equilibrium. Calculate the vertical component of…

Q: Problem 4. Fundamentals of Fluid Flow. Solve for the head added due to pump (in meters) for the…

Q: 2. A pipe carries water at a flow rate of 90 L/s. Determine the minimum inside diameter so that the…

Q: Obtain the volume of flow, in liters/sec, that will pass through a 600 mm pipe with a head loss of…

A: Diameter of pipe, D=600mmHead loss per kilometer, hfL=3m per KmCoefficient of friction, f=0.03

Q: Q.2.A.The closed tank in figure is at (20°c) (specific weight of air =0.0118 kN/m³). If the pressure…

Q: The fluid shown in figure has an absolute visco 0.0010 lb.sec/ft² and specific gravity of 0.913. the…

A: For the parabolic assumption, the parabola passes through the points v=0 when y=0 v=45 when y=3

Q: Three liquids given the following properties are poured into the cylindrical container with a…

A: To Find Pressure at 0.5 m above the tank bottom.

Q: For the flow field shown in figure find the flo properties M3, P3, T3 , Po3. 3 M1 = 2.5 Pi=100 Kpa…

A: At 1 the flow is isentropic flow: Using the isentropic table: At M=2 P1P10=0.1278P10=391.25 KPa

Q: Water of temperature 30o is flowing with flow rate 0.055 liters/s in a straight 50mm diameter uPVC…

A: Flow, Q=0.055 litres/s=0.055×10-3 m3/s diameter of pipe, d=50mm=0.05 m length of pipe, L=450 m HEAD…

Q: Problem 6 For the tank shown below (width = 1.25 m), determine (6.a) the maximum horizontal…

Q: 11- In an infinite two-dimensional flow filed, a sink of strength 3/2n m/s.m is located at the…

A: The given data is as follows: Strength of sink located at origin=32πm3/s.mStrength of another sink…

Q: 2. Estimate the pressure friction gradient in a 13.3 cm bore return tube for the following…

A: Fluid Pressure: Fluid pressure is a unit of force applied on the ever unit area Gravity,…

Q: Q3. (a) Determine the resulting hydrostatic force of water acting on the cylindrical wall of the…

Q: Q1: the pressure at point A is 172 pa. All fluids are at 20°C. The air pressure in the closed…

A: to find pressure at point B

Q: Problem 6 . For the tank shown below (width = 1.25 m), determine (6.a) the maximum horizontal…

Q: In fig. if h1= 0.5 m , h2= 1.5 m and the fluid y2 S.G= 13.6 , y1 is water, what is ?the pressure in…

Q: Assuming the flow into the tank is maintaining the water surface elevation at a constant location,…

A: Given - h = 0.20 m d = 0.01 m D = 0.20 m To find - The flowrate ?

Q: 2. For an incompressible and Newtonian flow, show that: 寸.ラ=AT

A: In fluid mechanics we have to derive the given expression as given in question according to…

Concept explainers

British Gravitational Bg System Of Units

Measuring is the comparison of a particular physical quantity with its reference value. A unit is a fixed physical quantity. The length is a physical quantity. A physical quantity is the product of a unit and the numerical value we need to compare with. 

Question

3.1 Derive the appropriate shallow water equations
for a single moving layer of fluid of density p1 above
a rigid floor, and where above the moving fluid is a
stationary fluid of density Po, where po < P1. Show
that as (Po/p1) → 0 the usual shallow water equa-
tions emerge.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

A storage tank contains a liquid at depth y where y=0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meets demands. The Contents are resupplied at a sinusoidal rate 30sin (t). Equation can be written as: d(Ay) = 3Q sin?(1) – Q (1)p (change in` (inflow) – (outflow) volume since the surface area A is constant sin²ce) – O A dy d(t) Use Euler's method to solve for the depth y from t = 0 to 10 d with a step size of 0.5 d. The parameter values are A = 1200 m? and Q = 500 m/d. Assume that the initial condition is y = 0.
Water backs up behind a concrete dam as shown in the Figure. Leakage under thefoundation gives a pressure distribution under the dam as indicated. If the water depth, h, is toogreat, the dam will topple over about its toe (Point A). The width of the dam is L and the heightof the dam is hd. Specific weight of the concrete is γc, the specific weight of the water is γw.Base your solution on a unit length of the dam. Sketch the free body diagram. Write the solutionprocedure step by step to determine the maximum water depth (h) in order not to cause anyoverturning about point A
A time independent non Newtonian fluid of density 0,00085kg/cm3 flows in a cylindrical pipe with a mean linear velocity of 1.70 m/s at steady state. The pipe is 3m long with an inside diameter of 0.075m. The point pipe consistency coefficient is 1.52 (N/m2)s0.3 and the flow behavior index is 0.3. Determine: a) The point values of the apparent viscosity. b) Reynolds Number. c) Pressure drop in Pascals.
A water siphon having a constant inside diame of 3 in. is arranged as shown in the figure below the friction loss between A and B is 0.8V²/2 wh is the velocity of flow in the siphon, determine flowrate involved. Assume a = 4 ft, h = 12 ft. D-- B a h
CORRECT LETTER PLS 1. In a system with 4 reservoirs and 1 pipe junctions, how many hydraulic headloss equations are formulate? A. 3B. 2C. 1D. 4E. 5 2. In turbulent flow, which is correct?BJ: higher Re value has lower friction factorJB: lower Re value has lower friction factorGroup of answer choices A. BJ is true and JB is false B. BJ is true and JB is true C. BJ is false and JB is false D. BJ is false and JB is true 3.which of the following is always the same for horizontal closed conduit? A. Total headB. Velocity headC. Elevation headD. Pressure head
Q3. SAE 30 oil (Sp. Gr. =0.833) with a dynamic viscosity 0.28 N.S/m? flows in a 4-cm-diameter pipe which is inclined with an angle 37°. For the pressure measurement shown, determine A. Whether the flow is up or down The flow rate in m'/h C. The shear stress and velocity 1 cm from the boundary Draw the shear stress and velocity profile with the section of the pipe. В. D. P-180 kPa P- sOokPa 15m 20m
A large plate is centrally placed inside a gap which contains two h different fluids with (u =4 u2 ). If the force per unit area due to shear acting on both side of plate is 50 N. Calculate the values of viscosity for the two fluids ( i.e p and u2). V= 0.5 m/sec 6 cm Plate
Incompressible steady flow in the inlet between parallel plates in the following figure is uniform,u=U0=az(zo-z),where a is a constant.If zo=4cm and the fluid is SAe 30 oil at 20°c ,What is the value of umax in cm/s?
An oil with p= 900 kg/m and v= in Fig. E6.4. The pressure and elevation are known at sections 1 and 2, 10 m apart. Assuming 0.0002 m'/s flows upward through an inclined pipe as shown d=6 cm 10 m Pz= 250,000 Pa 40 P 350,000 Pa, z =0 steady laminar flow, (a) vetify that the flow is up, (b) compute h, between I and 2, and compute (c) Q. (d) V, and (e) Re. Is the flow really laminar? pgd'h 128uL 2,431, Eu 66 70 & Density of Air p = 1.205 kg/m 364 S44 o176 = 15 11 o76 +rso k Coefficient of viscosity for air u = 1.80 x 10-5 K hy = 151 355m Force of gravity = 9.807 Density of water p= 998 kg/m3 Coefficient of viscosity (water) u = 0.001 kg/(m.s) For gasoline at 20°C, from the Table p= 680 kg/m'y = pg, g =9.81
If friction is neglected then the water ....... velocity value is unchanged increase decrease vena contracta has pressure .acroos the cross_sectional area high low constant a decrease in flow area in pipe .causes............ in pressure increase decrease stop
A tank contains gasoline sp. gr. = 0.90, oil sp. gr. = 0.8, and seawater sp.gr. = 1.03. If the depths of the liquids are 0.5 m. for oil, 0.6 m. gasoline, 1 mseawater. respectively. Find the pressure IN kPa at a depth of 1.4 m. Use 3decimal places.
The velocity profile of water(density 1000 kg/m and viscosity of 0.001 N.S/m² ) in a pipe is u%=²(R² -r²) where R is radius of the pipe and r is any distance from the center of the pipe. %3D The roughness of the pipe is 0.03 mm. i. If the pipe is replaced by another pipe with higher roughness of 0.075 mm, Calculate the pressure drop in two-meter length of the pipe. ii. evaluate the pressure drop in two-meter. ii. Explain your answers (difference or similarity) in parts (i) and (ii).