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Reynolds (1842-1912)

Ernst Mach (1838 – 1916). Reynolds (1842-1912). FORCES:. (in Fluid Mechanics). Viscous. Pressure. Gravity. Surface Tension. Compressibility. SIGNIFICANT DIMENSIONLESS GROUPS IN FLUID MECHANICS. Inertia. Viscous. Euler Number ( Eu = C p ). Pressure. Froude Number ( Fr ).

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Reynolds (1842-1912)

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  1. Ernst Mach (1838 – 1916) Reynolds (1842-1912)

  2. FORCES: (in Fluid Mechanics) Viscous Pressure Gravity Surface Tension Compressibility SIGNIFICANT DIMENSIONLESS GROUPS IN FLUID MECHANICS Inertia

  3. Viscous Euler Number (Eu = Cp) Pressure Froude Number (Fr) Gravity Weber Number (We) Mach Number (M) Compressibility Surface Tension PHYSICAL MEANINGS OF DIMENSIONLESS GROUPS Inertia Reynolds Number (Re) DIMENSIONLESS GRUOPS

  4. Must be Scaled EXPERIMENTAL DATA To calculate secondary data: - Forces - Moments, etc. - GEOMETRIC SIMILARITY: - KINEMATIC SIMILARITY: - DYNAMIC SIMILARITY: FLOW SIMILARITY AND MODEL STUDY There must be similarity between MODEL and PROTOTYPE - Similar in shape - Constant (linear) scales - Similar flow kinematics - Constant scales (in magnitudes) - All forces scaled constantly - Needs geometric & kinematic sim’s.

  5. FLOW SIMILARITY AND MODEL STUDY (Cont’d) For complete analysis All contributing forces must be presented: - Viscous force - Pressure force - Surface tension force - etc. Buckinghamp – theorem can be used

  6. r, m, V From p – theorem, we have: F D The flow will dynamically similar if: Similarity in the ratio of drag to inertia forces between model & prototype Also: Similarity in the ratio of inertia to viscous forces between model & prototype EXAMPLE Drag force analysis on a sphere: F = f (D, V, r, m)

  7. EXAMPLE PROBLEM 7.4 Given: Sonar transducer model tested in a wind tunnel Find: a) Vm b) Fp Solution: The test should be run at:

  8. EXAMPLE PROBLEM 7.4 5.02 x 105 Therefore: 5.02 x 105 And: Vm = 156 ft/sec  47.55 m/s Finally: Fp = 54.6 lbf

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