Chapter5 Lecture

# Chapter5 Lecture - Chapter 5 The First Law of...

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Chapter 5 The First Law of Thermodynamics for Open Systems 1. Discuss mass flow, volume flow, and flow work 2. Derive the First Law for Open Systems 3. Apply the first law to several steady open systems 4. Apply the first law to unsteady open systems

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Conservation of Mass Classical physics: Mass can not be created or destroyed. General format for the balance of a quantity in a system: Time rate of change of a quantity in a system = Transport rate into system through boundaries - Transport rate out of system through boundaries + Rate of quantity production in the system - Rate of quantity destruction in the system
Conservation of Mass For all systems, the production and destruction terms are zero for mass conservation For closed systems, the transport rate terms are also zero m cm For a closed system (or control mass), 0 dt dm cm We have already used the conservation of mass for the closed system.

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Conservation of Mass Open system: Can have various mass flows passing into and out of the system (control volume) outlets out inlets in cv m m dt dm The rate of change of mass in the system m cv Steady Flow outlets out inlets in cv m m dt dm 0
Velocity Vectors x y z V i ˆ j ˆ k ˆ u w v k w j v i u V ˆ ˆ ˆ

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Mass Flow Rate n ˆ How much mass flows through the shaded surface during one second? x y z k w j v i u V ˆ ˆ ˆ i n ˆ ˆ dA Flow direction
Volumetric and Mass Flow Rates in a Duct or Pipe Consider a small area element in a cross section of a duct/pipe: dA V n How much fluid volume passes through the area during a short time dt? dA V n dt Mass flow during time dt = mass in the cylinder = dm = ρ*V n *dt*dA n V V n Volume of cylinder

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Volumetric and Mass Flow Rates in a Duct/Pipe A n A n dA V V dA V m Rate of transport of mass through a channel of cross section A Rate of transport of fluid volume through a channel of cross section A m v m V For constant density (specific volume) across the cross-sectional area
Velocity Profiles in a Duct/Pipe x r Fully-developed velocity profile Microscopic roughness at the wall results in trapped stagnant fluid, u=0 at the wall Viscosity produces smoothly varying velocity profiles

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x r Represent the flow as uniform at the average velocity Mean Velocity A V m A dA V V m area n m A V m t=V m for Δt = 1 sec
Laminar flow in a round pipe has a velocity profile: ) ) ( 1 ( 2 max R r V V n Where R is the radius of the pipe, and r is the radial coordinate. x

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Chapter5 Lecture - Chapter 5 The First Law of...

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