Presentation on theme: "Experiment #5 Momentum Deficit Behind a Cylinder"— Presentation transcript:
1 Experiment #5 Momentum Deficit Behind a Cylinder
2 Problem Statement Water, 40 °F 2.0 mph 0.5” rod Find the drag force on the rod located in a 2.0 mph 40 °F water streamUse analogy with air flow normal to a model cylinder in a wind tunnelEstimate the error in the drag force0.5” rod
3 Available Major Equipment 6 x 6 inch in cross section wind tunnelHot film anemometer to measure air speedModel cylinder to place in the wind tunnel
4 Approach Measure the drag on a model cylinder in the wind tunnel Use results from dimensional analysis to establish the conditions for similarity between the flow around the model and the prototype (the rod in the water stream)Use the non-dimensional numbers derived from dimensional analysis to estimate the drag force on the rodEstimate the error in the drag force on the model and the prototype
5 Results from Dimensional Analysis (consult a fluids text) Drag Coefficient, CD,of a cylinder in cross-flowFD = drag force on the cylinderr = air densityD = cylinder diameterw = cylinder lengthU1 = approach velocity of air streamn = kinematic viscosity of airSimilarity between model and prototype requires thatCDmodel = CDprototype= f(Remodel) = f(Reprototype) or thatRemodel = Reprototype
6 Equality of Reynolds Numbers implies equality of the Drag Coefficients
7 Experimental Approach for the Drag Force Estimate the Reynolds number for the prototype (rod in water), and compute the wind tunnel air speed necessary for similarity with the model cylinderNote: account for the fact that the pressure in the wind tunnel is less than atmosphericFind the drag force on the model cylinder from measurements carried out in the wind tunnelCompute the model Reynolds number and Drag coefficient.Compare with the values from the previously shown CD vs. Re curve.Assuming similarity (check this) use the magnitude of the experimental drag coefficient on the model cylinder to find the drag force on the prototype stack
8 Static pressure inside the wind tunnel Use Bernoulli’s equation between points o (outside the tunnel) and 1 (inside the tunnel)Note that at point o the pressure is the atmospheric level, and that the velocity at point o is zero.Using the known wind tunnel speed, V1 find the pressure p1.
10 Control Volume Force and Mass Balances (r = constant) Force balanceSurface 1, rate of momentum inSurface 2,rate ofmomentum outSurfaces 3 and 4, rate ofmomentum outMassbalanceSurfaces 3 and 4, rate ofmass outSurface 1, rate ofmass inSurface 1, rateof mass outMultiplying the second eq. by U1 and substituting in the first eq, results in:
11 Drag force on the Model Cylinder Measure the velocity profile U1 without the cylinderMeasure the velocity profile u2 with the cylinderat two location downstream from the cylinderCompute FD for each of the two profiles using theexperimental data (numerical integration needed)Take the mean of the two FD values
13 Error EstimationFind the error in FD of the model assuming that the only measuring error is a ±1% in the measurement of velocity.Use the RSS method. (Consult your 650:350 Measurements Book)Error in FDwhereanduu2 and uU1 are the ± errors in the velocity measurement. Use ±1% of measured valuesNumerical integration is needed to evaluate the integrals
14 Error Estimation (continued) The error in the FD of the prototype rod is then found in a similar way from:
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