Obtain the energy equation from Euler's equation for an incompressible fluid
Take the Euler equation for an incompressible fluid of constant density, cast it into an appropriate form, and perform suitable operations on it to obtain the energy equation: d , pu’dv = --(p?+ {pu?)*•nds, where V is the region enclosed by a fixed closed surface S drawn in the fluid, and p' denotes p + PX, the non-hydrostatic part of the pressure field.
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Obtain the energy equation from Euler's equation for an incompressible fluid
In addition, derive the "wave equation" for an incompressible fluid. Use the continuity equation and the...
In addition, derive the "wave equation" for an incompressible
fluid. Use the continuity equation and the linearized euler
equation.
Linearized Euler:
A flow is incompressible if a fluid element does not change its density as the element moves. From Problem 54.1, this means (7p/dt) u . ρ-0. (a) Show that for an incompressible fluid the equation of continuity reduces to V -u -0. (b) Write Euler's equation for the flow of an incompressible fluid. (c) What is c for an...
For an ideal, incompressible fluid of density p, subject to a gravitational field g= -Vº' (here...
For an ideal, incompressible fluid of density p, subject to a gravitational field g= -Vº' (here Ø' is the gravitational potential) the Euler equation is: Div=-- Vp+g, Div = .v + (v.7)v Use vector identity v * (I xv) = -(v.7)v + rv2) to derive Bernoulli's equation: --v2--p - d' = const, along any streamline (dye path) in steady flow. (a) Use y (b) This question concerns free surface flow and hydraulic jumps. Incompressible inviscid fluid (water) is in steady,...
vector calculus (2) The Navier-Stokes equation is the fundamental equation of fluid dynamics that models the...
vector calculus
(2) The Navier-Stokes equation is the fundamental equation of fluid dynamics that models the motion of water in everything from bathtubs to oceans. In one of its many forms (incompressible, viscous flow), the equation is Ae +(V.V)V)-Vp+ p(V.V at In this notation V = (u, v, w) is the three-dimensional velocity field, p is the (scalar) pressure, p is the constant density of the fluid, and is the constant viscosity. Write out the three component equations of this...
Fluid Mechanics. Please answer as many as you can. Short answer questions 1) Explain the physical...
Fluid Mechanics. Please answer as many as you can.
Short answer questions 1) Explain the physical meaning of the acceleration term uVu, where u is the velocity vector in a fluid. 2) Name the two equations that are required to describe the flow of an inertial jet in an incompressible, unstratified fluid. 3) What is the “Continuum Hypothesis”? 4) Describe how a viscous boundary layer adjacent to a solid surface results in transfer of momentum to/from that surface. 5) What...
(Fluid mechanics) 2 of 3 Water, assumed inviscid and incompressible, flows steadily out of a large...
(Fluid mechanics)
2 of 3 Water, assumed inviscid and incompressible, flows steadily out of a large tank as shown in the adjacent figure. Above the water there is a 2-m layer of oil of specific gravity SG = 0.81 and the water outlet is located 0.7 m below the oil-water interface. Take the elevation reference (z = 0) at the outlet level. Determine: Oil, SG = 0.81 0.7 m Water 50 mm diameter a) Are the validity conditions of Bernoulli's...
2. The acceleration equation We have derived in lectures the Friedmann and fluid equations, that describe...
2. The acceleration equation We have derived in lectures the Friedmann and fluid equations, that describe the evolution of simple cosmologies. The Friedmann equation is usually given (adopting c 1) as where a(t) is the scale factor of the universe, p is the mass (energy) density, and k is constant. (a) (5 points) The simplest (although spectacularly uninteresting) cosmology has zero mass-energy, i.e. ρ 0. Solve the Friedmann equation under this condition to obtain an expression for at(t). Describe the...
could you please help me with answering all parts of this question. like and comment are...
could you please help me with answering all parts of this question.
like and comment are rewarded.
[7] A3. (a) Draw the streamlines and vortex lines of a Rankine vortex. Indicate which field lines are streamlines and which field lines are vortex lines, and label the vortex core. Explain which region of the flow has zero vorticity, and which region of the flow has non-zero vorticity. (b) A fluid with constant density po, pressure p, and velocity v, satisfies the...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is such that water flows through a pipe, exhibiting a laminar and steady-state flow. At the top end of the pipe, the flow tube has a cross-sectional area A and point 1 (located on the central streamline) is exposed to the ambient environment. The pipe drops through a A vertical distance h7 while its area decreases to when it reaches point 2 (also on the...
You are working in a new and not very well understood area of fluid You wish...
You are working in a new and not very well understood area of fluid You wish to predict the power delivered by a turbine, and you kn dynamics, such as fluid flow through very low permeability the outer and inner diameters of the wheel, the angle of the guid formations. You would like to build a laboratory model and use the vanes, the discharge (another term for volumetric flow rate), wa measurements you obtain there to understand the real word...
Question 1 Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8:...
Question 1
Question 2:
Question 3:
Question 4:
Question 5:
Question 6:
Question 7:
Question 8:
Please number each question. Thank you
Question 1 Not yet answered Marked out of 4.00 Flag question If the number density of electrons in a wire is n 1.00 x 1028 m-3, at what drift velocity must they travel through a wire of diameter d 0.560 mm to deliver a current of 7.20 A? Give your answer in mm s1 to 3 significant figures...
In addition, derive the "wave equation" for an incompressible
fluid. Use the continuity equation and the linearized euler
equation.
Linearized Euler:
A flow is incompressible if a fluid element does not change its density as the element moves. From Problem 54.1, this means (7p/dt) u . ρ-0. (a) Show that for an incompressible fluid the equation of continuity reduces to V -u -0. (b) Write Euler's equation for the flow of an incompressible fluid. (c) What is c for an...
For an ideal, incompressible fluid of density p, subject to a gravitational field g= -Vº' (here Ø' is the gravitational potential) the Euler equation is: Div=-- Vp+g, Div = .v + (v.7)v Use vector identity v * (I xv) = -(v.7)v + rv2) to derive Bernoulli's equation: --v2--p - d' = const, along any streamline (dye path) in steady flow. (a) Use y (b) This question concerns free surface flow and hydraulic jumps. Incompressible inviscid fluid (water) is in steady,...
vector calculus
(2) The Navier-Stokes equation is the fundamental equation of fluid dynamics that models the motion of water in everything from bathtubs to oceans. In one of its many forms (incompressible, viscous flow), the equation is Ae +(V.V)V)-Vp+ p(V.V at In this notation V = (u, v, w) is the three-dimensional velocity field, p is the (scalar) pressure, p is the constant density of the fluid, and is the constant viscosity. Write out the three component equations of this...
Fluid Mechanics. Please answer as many as you can.
Short answer questions 1) Explain the physical meaning of the acceleration term uVu, where u is the velocity vector in a fluid. 2) Name the two equations that are required to describe the flow of an inertial jet in an incompressible, unstratified fluid. 3) What is the “Continuum Hypothesis”? 4) Describe how a viscous boundary layer adjacent to a solid surface results in transfer of momentum to/from that surface. 5) What...
(Fluid mechanics)
2 of 3 Water, assumed inviscid and incompressible, flows steadily out of a large tank as shown in the adjacent figure. Above the water there is a 2-m layer of oil of specific gravity SG = 0.81 and the water outlet is located 0.7 m below the oil-water interface. Take the elevation reference (z = 0) at the outlet level. Determine: Oil, SG = 0.81 0.7 m Water 50 mm diameter a) Are the validity conditions of Bernoulli's...
2. The acceleration equation We have derived in lectures the Friedmann and fluid equations, that describe the evolution of simple cosmologies. The Friedmann equation is usually given (adopting c 1) as where a(t) is the scale factor of the universe, p is the mass (energy) density, and k is constant. (a) (5 points) The simplest (although spectacularly uninteresting) cosmology has zero mass-energy, i.e. ρ 0. Solve the Friedmann equation under this condition to obtain an expression for at(t). Describe the...
could you please help me with answering all parts of this question.
like and comment are rewarded.
[7] A3. (a) Draw the streamlines and vortex lines of a Rankine vortex. Indicate which field lines are streamlines and which field lines are vortex lines, and label the vortex core. Explain which region of the flow has zero vorticity, and which region of the flow has non-zero vorticity. (b) A fluid with constant density po, pressure p, and velocity v, satisfies the...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is such that water flows through a pipe, exhibiting a laminar and steady-state flow. At the top end of the pipe, the flow tube has a cross-sectional area A and point 1 (located on the central streamline) is exposed to the ambient environment. The pipe drops through a A vertical distance h7 while its area decreases to when it reaches point 2 (also on the...
You are working in a new and not very well understood area of fluid You wish to predict the power delivered by a turbine, and you kn dynamics, such as fluid flow through very low permeability the outer and inner diameters of the wheel, the angle of the guid formations. You would like to build a laboratory model and use the vanes, the discharge (another term for volumetric flow rate), wa measurements you obtain there to understand the real word...
Question 1
Question 2:
Question 3:
Question 4:
Question 5:
Question 6:
Question 7:
Question 8:
Please number each question. Thank you
Question 1 Not yet answered Marked out of 4.00 Flag question If the number density of electrons in a wire is n 1.00 x 1028 m-3, at what drift velocity must they travel through a wire of diameter d 0.560 mm to deliver a current of 7.20 A? Give your answer in mm s1 to 3 significant figures...
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