Page ES 202 Fluid and Thermal Systems Exam 1 Review Session 1 11 03 Conservation and accounting principles o mass mass transfer without generation o momentum mass transfer force transfer without generation classification of force body force surface force classification of surface force normal force shear force o energy mass transfer heat transfer work transfer without generation o entropy mass transfer heat transfer with generation Objectives design and modeling assumptions of steady state devices o nozzle diffuser o compressor turbine o valve o heat exchanger Concept of pressure o surface normal force o the only surface force when a fluid is at rest o same magnitude in all directions at a point Hydrostatic distribution of pressure o does not vary in horizontal direction o increases linearly with depth proportional to fluid density dP g dy Applications o manometer o Pitot static tube flow speed measurement device o multiple layer of fluids Force and moment calculations o by first principles direction integration on arbitrary shape o by formula for common surface shapes Force analysis o concept of centroid F Pc A where Pc is the pressure at the geometric center centroid of submerged surface Moment analysis o concept of line of action of resultant force center of pressure o center of pressure always lies below the centroid y p yc I xx c yc A offset 1 Page Applications o plane surfaces vertical horizontal and inclined o curved surfaces horizontal force component is the same regardless of shape as long as vertical projection of submerged surface is the same vertical force component depends on the amount of fluid above below the surface Origin of buoyancy force Quantification of buoyancy force Archimedes principle o magnitude equals the weight of fluid displaced by submerged body o direction is always upward through the centroid of displaced volume Classification of fluid energy o mechanical energy o thermal energy Fundamental difference between them Components of mechanical energy o flow work pressure energy o kinetic energy o potential energy Mechanical energy balance o derived from general energy balance and extract out the mechanical energy term P V2 P V2 gz wout losses gz win 2 2 out in Conservation of mechanical energy leads to Bernoulli s equation P o V 2 2 gz constant interpreted as interchange of mechanical energy among its various components while keeping their sum to be constant Assumptions of Bernoulli s equation Strategy in problem solving o apply conservation of mass to relate unknown velocities o apply Bernoulli s equation to relate unknown pressures Modified Bernoulli s equation as a correction for viscous losses V 2 V 2 P gz P gz ghL 2 2 up down Concept of stagnation pressure o as a measure of total loss in a system 2 Page Concept of viscosity as fluid friction Distinction between laminar and turbulent flow Estimation of total loss in system o major loss due to friction on single straight pipe surface P f o L V 2 D 2 introduction of friction factor as a non dimensional group functional dependency of friction factor Moody diagram Haaland formula Colebrook formula types of design problem specify mass flow rate determine pressure drop specify pressure drop determine mass flow rate more difficult o requires iterative solution minor loss due to friction in flow direction changes exit entrance connection turn P K L V 2 2 introduction of loss coefficient KL as a non dimensional group tabulation of empirically determined values of KL Strategy to estimation of total loss o follow a divide and conquer approach o identify sources of loss o express individual major and or minor loss o sum up pressure difference to get total loss pressure differences are additive telescoping effect Pipe system o series configuration same mass flow rate throughout o parallel configuration same pressure drop across each pipe section Dimensional analysis o Buckingham Pi Theorem o representation of functional relationship in non dimensional space 3