BLDG 365 Building Science2021-03-14Chang-Seo Lee1BLDG365 Building ScienceFluid MechanicsWinter 2021Chang-Seo Lee, PhD, PEngConcordia University1Part A. Fluid Mechanics Basics 212
BLDG 365 Building Science2021-03-14Chang-Seo Lee2Buildings and Fluid FlowNatural air flow in buildingsWind and buildingsAir conditioning and buildingsVentilation and buildingsHeating and coolingFresh air Outdoor airHot and cold water flowSteam flow3Basic PrinciplesYou need to have a pressure difference to have fluid flowFluid flows from high pressure environment to low pressure environmentMass is conserved (not lost)Momentum is is conserved (not lost)Energy is is conserved (not lost)434
BLDG 365 Building Science2021-03-14Chang-Seo Lee3Continuity EquationConservation of Massthe mass flow rate into a section of pipe must equal the mass flow rate out of that section of pipe if no mass is accumulated or lost𝑚̇ = න 𝜌𝑣𝑑𝐴 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡ṁ = mass flow rate across the area normal to flow, v = fluid velocity normal to differential area dA= fluid densityFor incompressible flow (= constant) Average velocity (𝑣̅): 𝑣̅ =ଵ∫ 𝑣𝑑𝐴Mass flow rate (ṁ): 𝑚̇ = 𝜌𝑣̅𝐴Volumetric flow rate (Q): 𝑄 =̇ఘ= 𝑣̅𝐴5Note: u, v , U, V are referring velocity – the notation follows the notation used in figure in each slideBernoulli’s equation (1700-1782)Law of conservation of energy sum of the kinetic energy, energy due to pressure and potential energy (i.e. the total energy) is always constant.Kinetic energy = ଵଶ𝜌𝑣ଶPotential energy = gzPressure energy = P656
BLDG 365 Building Science2021-03-14Chang-Seo Lee4Bernoulli’s equation𝑃 +ଵଶ𝜌𝑣ଶ+ 𝜌𝑔𝑧 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡P: Static Pressureଵଶ𝜌𝑣ଶ: Dynamic Pressuregz: Hydrostatic PressureTotal Pressure: sum of the static, dynamic, and hydrostatic pressuresIf variation in height above the datum is zero or negligible, the sum of the static and dynamic pressures is the total pressureStagnation Pressure: sum of the static and dynamic pressures 𝑃ଵ+12𝜌𝑣ଵଶ+ 𝜌𝑔𝑧ଵ= 𝑃ଶ+12𝜌𝑣ଶଶ+ 𝜌𝑔𝑧ଶ7Bernoulli’s equation𝑃𝜌𝑔+𝑣ଶ2𝑔+ 𝑧 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 𝐻P/g = Pressure HeadV2/2g = Velocity Headz = Elevation Head (or simply “Head”)H = Total Head𝑃ଵ𝜌𝑔+𝑣ଵଶ2𝑔+ 𝑧ଵ=𝑃ଶ𝜌𝑔+𝑣ଶଶ2𝑔+ 𝑧ଶThe sum of the pressure, velocity, and elevation heads along a streamline is constant during steady flow when compressibility and frictional effects are negligible.878
BLDG 365 Building Science2021-03-14Chang-Seo Lee5Limitations on the Use of the Bernoulli Equation1.Steady flowIt should not be used during the transient start-up and shut-down periods, or during periods of change in the flow conditions. Note that there is an unsteady form of the Bernoulli equation.2.Negligible viscous effectsFrictional effects are usually significant in long and narrow flow passages, in the wake region downstream of an object, and in diverging flow sections such as diffusers because of the increased possibility of the fluid separating from the walls in such geometries. Frictional effects are also significant near solid surfaces.