# BLDG365-#8-Fluid Mechanics-W2021-Handout.pdf - BLDG 365...

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BLDG 365 Building Science 2021-03-14 Chang-Seo Lee 1 BLDG365 Building Science Fluid Mechanics Winter 2021 Chang-Seo Lee, PhD, PEng Concordia University 1 Part A. Fluid Mechanics Basics 2 1 2
BLDG 365 Building Science 2021-03-14 Chang-Seo Lee 2 Buildings and Fluid Flow Natural air flow in buildings Wind and buildings Air conditioning and buildings Ventilation and buildings Heating and cooling Fresh air Outdoor air Hot and cold water flow Steam flow 3 Basic Principles You need to have a pressure difference to have fluid flow Fluid flows from high pressure environment to low pressure environment Mass is conserved (not lost) Momentum is is conserved (not lost) Energy is is conserved (not lost) 4 3 4
BLDG 365 Building Science 2021-03-14 Chang-Seo Lee 3 Continuity Equation Conservation of Mass the 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 lost 𝑚̇ = න 𝜌𝑣𝑑𝐴 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ṁ = mass flow rate across the area normal to flow, v = fluid velocity normal to differential area dA = fluid density For incompressible flow ( = constant) Average velocity ( 𝑣̅) : 𝑣̅ = ∫ 𝑣𝑑𝐴 Mass flow rate (ṁ): 𝑚̇ = 𝜌𝑣̅𝐴 Volumetric flow rate (Q): 𝑄 = ௠̇ = 𝑣̅𝐴 5 Note: u, v , U, V are referring velocity – the notation follows the notation used in figure in each slide Bernoulli’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 = 𝜌𝑣 Potential energy = gz Pressure energy = P 6 5 6
BLDG 365 Building Science 2021-03-14 Chang-Seo Lee 4 Bernoulli’s equation 𝑃 + 𝜌𝑣 + 𝜌𝑔𝑧 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 P: Static Pressure 𝜌𝑣 : Dynamic Pressure gz: Hydrostatic Pressure Total Pressure: sum of the static, dynamic, and hydrostatic pressures If variation in height above the datum is zero or negligible, the sum of the static and dynamic pressures is the total pressure Stagnation Pressure: sum of the static and dynamic pressures 𝑃 + 1 2 𝜌𝑣 + 𝜌𝑔𝑧 = 𝑃 + 1 2 𝜌𝑣 + 𝜌𝑔𝑧 7 Bernoulli’s equation 𝑃 𝜌𝑔 + 𝑣 2𝑔 + 𝑧 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 𝐻 P/ g = Pressure Head V 2 /2g = Velocity Head z = Elevation Head (or simply “Head”) H = Total Head 𝑃 𝜌𝑔 + 𝑣 2𝑔 + 𝑧 = 𝑃 𝜌𝑔 + 𝑣 2𝑔 + 𝑧 The sum of the pressure, velocity, and elevation heads along a streamline is constant during steady flow when compressibility and frictional effects are negligible. 8 7 8
BLDG 365 Building Science 2021-03-14 Chang-Seo Lee 5 Limitations on the Use of the Bernoulli Equation 1. Steady flow It 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 effects Frictional 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.
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