What is Control volume: Definition and 33 Discussions

In continuum mechanics and thermodynamics, a control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. In an inertial frame of reference, it is a fictitious volume fixed in space or moving with constant flow velocity through which the continuum (gas, liquid or solid) flows. The surface enclosing the control volume is referred to as the control surface.At steady state, a control volume can be thought of as an arbitrary volume in which the mass of the continuum remains constant. As a continuum moves through the control volume, the mass entering the control volume is equal to the mass leaving the control volume. At steady state, and in the absence of work and heat transfer, the energy within the control volume remains constant. It is analogous to the classical mechanics concept of the free body diagram.

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  1. C

    Trouble solving for end state of two control volumes in a rigid tank

    TL;DR Summary: Struggling to structure the problem and derive an analytical solution for gas expanding into other gas in a rigid tank. Preferred formulation is fixed control volumes. This is not a homework problem. The problem: Two control volumes (A and B) are in a rigid tank filled with air...
  2. George26

    Conservation of mass: control volume approach question

    Summary:: Control volume question that has a brine solution entering a tank and mass accumulates over time. Hello, I'm currently struggling with a control volume approach question that has a brine solution entering a tank. I get to a point where I have a first order differential equation. I...
  3. J

    How to control volume by hovering & scrolling anywhere in Mac Menu Bar

    Homework Statement:: How to control volume by hovering and scrolling anywhere in Mac Menu Bar Relevant Equations:: none Hi, 
 I use both Mac's and pc's. Mac's are great but here's one thing I can do in my pc's that I have not been able to find how to do in my Mac. 
 In my pc's (Win7, Win10)...
  4. A

    Bernoulli's equation from an elemental fixed streamtube control volume

    Elemental fixed streamtube control volume from Professor White’s textbook “Fuid Mechanics”: I was unable to develop the intermediate steps for the following approximations: (continuity equation according to the book ) Where and (Momentum equation according to the book) In...
  5. A

    Thermodynamics energy balance for control volume

    Why is energy balance for a control volume dE/dt = dQ/dt-dW/dt-dm/dt(ΔH+ΔKE+ΔPE) 0 = dQ/dt-dW/dt-dm/dt(ΔH+ΔKE+ΔPE) whereas for other systems it is ΔE =Q-W-(ΔU+ΔKE+ΔPE) 0 = Q-W-(ΔU+ΔKE+ΔPE) with enthalpy, h = u +pv, replaced by only the internal energy? How is the pv term accounted for...
  6. A

    Control volume and the momentum theorem

    I'm studying fluid and propulsion mechanics by myself. I stumbled upon this website from MIT: http://web.mit.edu/16.unified/www/SPRING/propulsion/UnifiedPropulsion2/UnifiedPropulsion2.htm#fallingblock It states that "Newton’s second law for a control volume of fixed mass" is $$\sum...
  7. K

    Control Volume, Fluid Mechanics

    Homework Statement Water flows over a dam as depicted below. Across section 1 and 2 we have a hydrostatic pressure distribution. Calculate the force on the dam. The Attempt at a Solution My question is regarding control volume. The solution manual has given us this: The two hydrostatic...
  8. K

    Control volume, Fluid mechanics

    Homework Statement I have a situation as illustrated by the image above, where the red box illustrates the CV. The pressure on the left side of CV is P1, while the pressure on the right side of CV is P2. Here I´ve directed the pressure forces acting inwards on CV. The problem arises with Fk. I...
  9. K

    Can't understand how flow work is possible in a control volume

    I am struggling to fully grasp the concept of flow work for a non-deformabable control volume. Nearly every source puts it in this way: flow work is the work required to push fluid into and out of the control volume and as such is defined as Pv on a unit mass basis. But how can this work be...
  10. AGiantGolden49er

    Thermodynamics Power Cycle Energy Balance

    Homework Statement As shown in Fig. P5.39, a system undergoing a power cycle develops a net power output of 1 MW while receiving energy by heat transfer from steam condensing from saturated vapor to saturated liquid at a pressure of 100 kPa. Energy is discharged from the cycle by heat transfer...
  11. O

    Control Volume of single expansion ramp nozzle (SERN)

    Hi guys, I need to determine the performance of a single expansion ramp nozzle (SERN) from CFD results with different nozzle pressure ratios (NPR). For some NPR the nozzle is overexpanded and for some underexpanded. Now the impact of the control volume definition on especially the axial thrust...
  12. H

    Is this equation conservative or non-conservative?

    Homework Statement This is the Navier-Stokes equation for compressible flow. nj is the unit normal vector to the surface 'j', and ni is the unit normal vector in the 'i' direction. Is this equation written for a control volume or a material volume? Homework Equations The Attempt at a...
  13. R

    Power consumption for maintaining Temp in a control volume

    Homework Statement Question 1: An insulated 8-m3 rigid tank contains air at 600 kPa and 400 K. A valve connected to the tank is now opened and air is allowed to escape until the pressure inside the tank drops to 200 kPa. The air temperature is maintained constant by an electric heater during...
  14. A

    Use of Entropy for a Control Volume in Energy Balance

    Hi all, I'm having some trouble figuring out why entropy is used instead of enthalpy for an open system. From what I understand, an open system uses entropy to calculate internal energy. Since the control volume is constant (i.e. Δv = 0), wouldn't using : h = u + PΔv effectively be h = u? So...
  15. P

    Thermodynamics Control Volume evaluation 2 inlet

    Figure P6.95 provides steady-state test data for a control volume in which two entering streams of air mix to form a single exiting stream. Stray heat transfer and kinetic and potential energy effects are negligible. A hard-to-read photocopy of the data sheet indicates that the pressure of the...
  16. K

    Determine the launching speed of the object

    So this is probably a very basic question. I'm studying EE so this is kind of out of my field as i have never taken this but I'm working on a project and it involves a pressurized container releasing air into a tube and launching something out the nozzle. The problem I'm having is that I'm not...
  17. P

    Pressure force on a control volume

    Homework Statement http://postimg.org/image/4a8sv6umh/ Why do the pressure forces due to p1 and p2 act in the same direction? Homework EquationsThe Attempt at a Solution I thought that, given the direction of the flow, the pressure force on the bottom and top would act in opposite directions
  18. P

    Momentum relation for control volume

    Homework Statement http://postimg.org/image/i4p19540z/ Homework Equations Resultant force on the control volume = Mass flow rate (Velocity outlets -Velocity inlets) The Attempt at a Solution I am just wondering if the 4cm is called depth, then what is the term for the "into the paper"...
  19. B

    Formulating the control volume for a mechanical system

    Folks, I am having difficulty correctly representing a mechanical system within a correct "control volume at an instant" in order to identify the various energy balance terms given below ##\displaystyle \dot E_{st}=\frac{d E_{st}}{dt}=\dot E_{in} - \dot E_{out}+ \dot E_g## (1) that...
  20. T

    Control Volume: Linear Momentum

    Homework Statement I know how to apply the linear momentum equation for the control volume, but I am not sure why the V2 (velocity of flow from section 2) is V*cos(60). The only reason I can see is the velocity being constant. And since there are two outlet with equal area, the velocity is...
  21. P

    Momentum for a control volume (Fluid Mechanics)

    Homework Statement http://i988.photobucket.com/albums/af10/postop/equationsmomentum_zpse8c8d44a.png Homework Equations The Attempt at a Solution Can somebody explain to me in the two equations above what is the "u" and what is the "v"? In the question, it says that the water at...
  22. M

    What Factors Should Be Considered When Choosing a Control Volume?

    Hello, My professor did a lecture about mass conservation in a system. He basically explained the lining that separates the system from the surroundings is the control surface, and all that is contained within the system is the control volume. I think it was explained rather loosely, and...
  23. A

    How does the angle of the plate affect the fraction of liquid that flows up?

    Homework Statement A horizontal water jet produces a wide sheet of parallel-flowing liquid that strikes an inclined plate and then divides, with a fraction of the liquid flowing up the plate and the remainder flowing down the plate. The figure shows a section of the flow. All surfaces of the...
  24. A

    Control volume, steady- state and steady-flow devices, enthelpy

    Homework Statement Air is to be compressed from 120 kPa and 310 K to 700 kPa and 430 K. A heat loss of 20 kj/kg occurs during the compression process. For air: cv=0.7165 kj/kg.K and R=0.287 kj/kg.K . A) Neglecting kinetic energy changes determine the power input required for a mass flow...
  25. Q

    Energy and Mass Analysis of a Control Volume

    Homework Statement Consider a system in which R 134-A is moved through an evaporator. The evaporator removes energy from the the surroundings at a rate of 0.54 kW. The pressure = 120 kPa and x = 0.2 right before the fluid enters the evaporator. After exiting the evaporator, the pressure = 120...
  26. V

    Analyzing Control Volume Energy & Entropy in a Vortex Tube

    Homework Statement Prior to completing an experiment in which the objective was to analyze control volume energy and entropy in a vortex tube in the Thermal and Fluid Science Laboratory course I am taking, I was required to solve the following two thermodynamics problems: 1. A vortex tube...
  27. M

    Control volume flux problem

    Homework Statement The velocity components of a flow are given by: u=-x v=y Compute the volume of fluid flowing per unit time per unit area through a small surface at (1,2) whose normal makes an angle of 60 deg with the positive x-axis. Homework Equations V= u i + y j (velocity vector)...
  28. A

    Thermodynamics: Control Volume flow through radiatior

    Homework Statement Air enters a car radiator at 50 km/hr, 25 C. The radiator is 1 m2 facial area. 2 kg/s of water enters the radiator from the engine at 10 bar, 200 C and leaves at 10 bar, 180 C. What is the temperature of the air as it leaves the radiator? Homework Equations I did...
  29. A

    Thermodynamics: Control Volume analysis using energy

    Homework Statement Steam flows through an uninsulated pipe at 0.5 kg/s, entering at 5 bar, 440 C and exiting at 3 bar, 320 C. How much energy is lost from the steam per hour? Homework Equations Which terms in the energy eqn can drop out? I'm having trouble with that. Is there only...
  30. V

    What is the role of control volume in the Navier-Stokes equations?

    navier-stokes smoothness problem almost solved Penny Smith has made progress with showing that smooth conditions exist for all time in a domain for the Navier Stokes equations http://notes.dpdx.net/2006/10/06/penny-smiths-proof-on-the-navier-stokes-equations/ However a flaw was found in the...
  31. S

    Adding remote control volume to old amplifier.

    Found the site doing a Google search. Just need to know if this is possible. I have an old amplifier that does not have any remote control. I wondered if it would be possible to do something that will alow me to at least control the volume remotely. Any ideas. Thanx.