A Presentation on Continuity, Momentum and Energy Equation Enrolment No Submitted By :Name Gohil Kiran R. Kadam Harshal P. Panchal Parth H. Rane Vaibhav S. Sathwara Vipul P. Savaliya Nitin J. B.E. Sem – 5 th Heat Transfer Year : Mechanical Engineering Department Government Engineering College Dahod

Energy Equation  In open system fluid flow is may be two types. 1.Steady flow 2.Unsteady flow  Steady flow means that the rate of flow of mass and energy across the controlled surface are constant.  Unsteady flow means that the rate of flow of mass and energy across the controlled surface are does not constant.

1. The mass flow rate remains constant within the system, i.e. mass entering the control volume must be equal to the mass leaving it and do not very with time. 2. The state of fluid at any fixed point in control volume is same and do not vary with time. 3. The state of energy of the fluid at entrance and exit of the control volume does not vary with time. 4. Heat and work transfer rate across the control surface does not vary with time. 5. Chemical composition of fluid within the control volume is fixed.  When any flow process does not satisfy the above condition of steady state, the process is known as unsteady flow process. The steady flow process is characterized by the following condition in control volume

Derivation energy equation  Consider flow of fluid through generalized open system as shown in figure. the working fluid enter the system at section 1 and leave the system at section 2 and passing at a steady rate. Sr No At inlet section 1-1At inlet section 2-2 1Mass flow rate, Kg/s 2Specific internal energy, J/Kg 3 4 5Velocity, m/sec 6Elevation above an arbitrary datum, m 7Potential energy / mass, Kj/kg 8Kinetic energy / mass, Kj/Kg 9Flow work, Kj/Kg 10Net rate of heat transfer through system J/KgQ 11Work done by systemW Let,

Datum System Fluid In Fluid Out Open System 1 2 Control Surface Control Volume (C.V) C.V. = Control volume q = Heat entering the control volume per kg of fluid, kJ/kg. w = Work transferred from the control volume per kg of fluid, kJ/kg.

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Application of SFEE

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Momentum Equation 

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 Consider a fluid flow through steam tube as shown in figure.  The fluid flow is assumed to be steady, uniform and normal to the inlet area PQ and outlet area RS. According to the principle of mass conservation. Mass flow rate through a control volume PQRS. P R QS

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Application of the momentum equation  We will consider the following examples :  Impact of jet on a plane surface.  Force due to flow round a curved vane.  Force due to the flow of fluid round a pipe bend.  Reaction of jet.

Continuity equation  The equation base on the principle of conservation of mass called as continuity equation.  Fluid flowing through the pipe at all the cross section, the quantity of fluid per second remain constant.  Consider fluid flow through the pipe as shown in figure 1122 pipe

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References :-  Books : - I. Engineering thermodynamics By J.P. Hadiya, H.G. Katariya – Books India publication II. Engineering thermodynamics By C.M. Desai, R.B. Varia – Atul publication III. Fluid mechanics and hydraulic machines By I.D. Patel, N.J. parmar - Atul publication  Websites :- I. re%205.pdf re%205.pdf II. on.pdf on.pdf