Derive a discretized form of the generic integral form of the continuity, momentum and energy equations...
Derive a discretized form of the generic integral form of the continuity, momentum and energy equations obtained in Prob 2.2. The discretized form is the essense of the finite volume approach. ( Prob 2.2: Derive the momentum and energy equations for a viscous flow in integral form. Show that all three conservation equations--continuity momentum, and energy-can be put in a single generic integral form.)
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Derive a discretized form of the generic integral form of the
continuity, momentum and energy equations...
Deduce a set of boundary-layer differential equations (continuity, momentum, energy) for steady f...
Deduce a set of boundary-layer differential equations
(continuity, momentum, energy) for steady flow of a
constant-property fluid without body forces, and with negligible
viscous dissipation, in a coordinate system suitable for analysis
of the boundary layer on the surface of a rotating disk
Problem # 6 Deduce a set of boundary-layer differential equations (continuity, momentum, energy) for steady flow of a constant-property fluid without body forces, and with negligible viscous dissipation, in a coordinate system suitable for analysis of the...
Momentum Theory Use one-dimensional conservation of momentum together with conservation of mass (continuity) and energy (Bernoulli’s...
Momentum Theory Use one-dimensional conservation of momentum together with conservation of mass (continuity) and energy (Bernoulli’s equation = mechanical energy) to derive the power an ideal, frictionless wind turbine with an infinite number of blades, uniform thrust over the rotor area and a non-rotating wake can extract from the wind. Formulate the derivation in terms of the fractional decrease in wind velocity between the velocity far upstream and at the turbine rotor, ? = (? − ?)/?, also called “axial...
Bernoulli equation. The Bernoulli equation is a special case of conservation of linear momentum law of...
Bernoulli equation. The Bernoulli equation is a special case of conservation of linear momentum law of conservation of energy) for steady frictionless flow. This equation can be arrived at in three different ways. The usual form of the Bernoulli equation is: 1. pv2 + P + ?9z-constant a) For frictionless flow at steady state, Euler's equation of conservation of linear momentum reduces to: Starting from this equation, derive the Bernoulli equation. Assume irrotational flow. Derive the Bernoulli equation using the...
Using the Energy Integral Equation (EIE), derive an expression for the average Nusselt number (in terms...
Using the Energy Integral Equation (EIE), derive an expression for the average Nusselt number (in terms of Reynolds and Prandtl numbers) for laminar flow of a fluid over a surface with a free stream velocity of U. (which is a constant). Assume the fluid velocity in the momentum boundary layer is the same as the free stream velocity and (T-Tw)/(To-Tw)=(y/St), where T is the fluid temperature field in the thermal boundary layer, To is the free stream temperature, Twis the...
C. Noether Theorem. In class we discussed how conservation of total momentum, angular momentum and energy...
C. Noether Theorem. In class we discussed how conservation of total momentum, angular momentum and energy are consequences of certain symmetries of the Lagrangian. More generally assume now that under a transformation of the form qi qi + eK (9), the lagrangian L = L(9.4) is invariant (meaning dL/de = 0). The functions Ki are functions of all the qi (denoted here collectively by 9). 1) Show that, if the Euler-Lagrange equations are satisfied then the quantity p(g, g) =...
BIG UPVOTE FOR RIGHT ANSWER Viscous fluid flow 2nd edition Frank White I need answer of...
BIG UPVOTE FOR RIGHT ANSWER
Viscous fluid flow 2nd edition Frank White
I need answer of 2.17
I have attached 2.14 question and solution for reference.
2.17 As an extension of Prob. 2-14, consider the heat-transfer
aspect by assuming a uniform entrance profile T = To and an exit
profile approximated by T(r) = T0(1.5 + 0.5r2/ri). For flow with
constant (p, F, cp, k) and negligible kinetic- and potential-energy
changes, use the integral relations to compute the total heat...
5. (Hints: This derivation is presented in your textbook briefly. I also discussed that in the cl...
plz if you could make it clear.
will thumb up
5. (Hints: This derivation is presented in your textbook briefly. I also discussed that in the class. I would like you to provide step-by-step process for this mathematical derivation. You need to use the continuity equation (Eq. 6-21) for the derivation process) Starting from the first law of Thermodynamics for a differential control volume, derive the general governing equation for temperature (6-35) for a 2D flow over flat plate. Using...
2. The equations of motion for a system of reduced mass moving subject to a force...
2. The equations of motion for a system of reduced mass moving subject to a force derivable from a spherically symmetric potential U(r) are AF –102) = (2+0 + rē) = 0 . (3) Using the second of these equations, show that the angular momentum L r 8 is a constant of the motion (b) Then use the first of these equations to derive the equation for radial motion in the form dU L i=- What is the significance of...
Please make the hand writing legible. Thanks Consider the situation depicted below, in which an incompressible...
Please make the hand writing legible. Thanks
Consider the situation depicted below, in which an incompressible fluid flows over a flat surface of solid. Upstream of the surface, the fluid has velocity U and uniform temperature To. As the fluid is viscous, both a momentum boundary layer, and a thermal boundary layer form, and heat is transferred to the solid surface. A convective coefficient h can be used to describe the dimensional heat transfer rate to the solid, and is...
Please show all the steps and calculations, thanks Problem 5.4 A short circular pipe with diameter...
Please show all the steps and calculations, thanks
Problem 5.4 A short circular pipe with diameter D, has water (p,u) flowing through it from left to right at a volumetric flow rate Q. At the exit a plug with diameter D2 that partially blocks the water flow is inserted (to provide upstream pressure pı (gage) to the pipe and/or to reduce flow rate). Both upstream pressure and flow rate can be measured. (a) Using the conservation equations (mass, momentum) in...
Deduce a set of boundary-layer differential equations
(continuity, momentum, energy) for steady flow of a
constant-property fluid without body forces, and with negligible
viscous dissipation, in a coordinate system suitable for analysis
of the boundary layer on the surface of a rotating disk
Problem # 6 Deduce a set of boundary-layer differential equations (continuity, momentum, energy) for steady flow of a constant-property fluid without body forces, and with negligible viscous dissipation, in a coordinate system suitable for analysis of the...
Bernoulli equation. The Bernoulli equation is a special case of conservation of linear momentum law of conservation of energy) for steady frictionless flow. This equation can be arrived at in three different ways. The usual form of the Bernoulli equation is: 1. pv2 + P + ?9z-constant a) For frictionless flow at steady state, Euler's equation of conservation of linear momentum reduces to: Starting from this equation, derive the Bernoulli equation. Assume irrotational flow. Derive the Bernoulli equation using the...
Using the Energy Integral Equation (EIE), derive an expression for the average Nusselt number (in terms of Reynolds and Prandtl numbers) for laminar flow of a fluid over a surface with a free stream velocity of U. (which is a constant). Assume the fluid velocity in the momentum boundary layer is the same as the free stream velocity and (T-Tw)/(To-Tw)=(y/St), where T is the fluid temperature field in the thermal boundary layer, To is the free stream temperature, Twis the...
C. Noether Theorem. In class we discussed how conservation of total momentum, angular momentum and energy are consequences of certain symmetries of the Lagrangian. More generally assume now that under a transformation of the form qi qi + eK (9), the lagrangian L = L(9.4) is invariant (meaning dL/de = 0). The functions Ki are functions of all the qi (denoted here collectively by 9). 1) Show that, if the Euler-Lagrange equations are satisfied then the quantity p(g, g) =...
BIG UPVOTE FOR RIGHT ANSWER
Viscous fluid flow 2nd edition Frank White
I need answer of 2.17
I have attached 2.14 question and solution for reference.
2.17 As an extension of Prob. 2-14, consider the heat-transfer
aspect by assuming a uniform entrance profile T = To and an exit
profile approximated by T(r) = T0(1.5 + 0.5r2/ri). For flow with
constant (p, F, cp, k) and negligible kinetic- and potential-energy
changes, use the integral relations to compute the total heat...
plz if you could make it clear.
will thumb up
5. (Hints: This derivation is presented in your textbook briefly. I also discussed that in the class. I would like you to provide step-by-step process for this mathematical derivation. You need to use the continuity equation (Eq. 6-21) for the derivation process) Starting from the first law of Thermodynamics for a differential control volume, derive the general governing equation for temperature (6-35) for a 2D flow over flat plate. Using...
2. The equations of motion for a system of reduced mass moving subject to a force derivable from a spherically symmetric potential U(r) are AF –102) = (2+0 + rē) = 0 . (3) Using the second of these equations, show that the angular momentum L r 8 is a constant of the motion (b) Then use the first of these equations to derive the equation for radial motion in the form dU L i=- What is the significance of...
Please make the hand writing legible. Thanks
Consider the situation depicted below, in which an incompressible fluid flows over a flat surface of solid. Upstream of the surface, the fluid has velocity U and uniform temperature To. As the fluid is viscous, both a momentum boundary layer, and a thermal boundary layer form, and heat is transferred to the solid surface. A convective coefficient h can be used to describe the dimensional heat transfer rate to the solid, and is...
Please show all the steps and calculations, thanks
Problem 5.4 A short circular pipe with diameter D, has water (p,u) flowing through it from left to right at a volumetric flow rate Q. At the exit a plug with diameter D2 that partially blocks the water flow is inserted (to provide upstream pressure pı (gage) to the pipe and/or to reduce flow rate). Both upstream pressure and flow rate can be measured. (a) Using the conservation equations (mass, momentum) in...
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