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day09_flow_3 - Ultimately, e.g,Chapter7: Continuity...

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1 Volume and mass flow rates Continuity Reminder of vapor pressure Ultimately, we need different techniques for engineering fluid dynamics problems y e.g., Chapter 7: How do we choose the pump based on measurements given for the figure shown: y We need Bernoulli for pressure variations, etc. and “conservation equations” for local flow information y e.g., Chapter 5: What is the concentration of fertilizer in the output of the spreader shown? Ultimately, we need different techniques for engineering fluid dynamics problems y We need Bernoulli for pressure variations, etc. and “conservation equations” for local flow information Liquid fertilizer with the same density as the water in the venturi section Volume and mass discharge Imagine a wire ring With cross section A m 2 A Place this ring in so that it area is normal to a fluid flow of average speed V m/s V Fluid Volume passing through the ring per second n If the ring is placed at an angle to the flow Mass Rate crossing the surface is v Q = VA m 3 /s A cos v A Q θ = = n v Q m ρ = & Variable flow calculations y Uniform flow calculations A cos v A cos vN A Q θ = θ = = n v y If flow is non uniform across the surface: ( ) θ = A cos v Q ( ) A cos v Q θ = ( ) θ A dA cos v 5.12 (8 th ed) 5.16 (9 th ed) y Air enters this square duct at section 1 with the velocity distribution as shown. Note that the velocity varies in the y direction only (for a given value of y, the velocity is the
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