1 / 9

Understanding Forces in Fluid Mechanics & Dimensionless Groups

Learn about the significance of dimensionless groups like Reynolds, Euler, Froude, Weber, and Mach Numbers in fluid mechanics. Discover how geometric and kinematic similarities are crucial for model studies to calculate forces accurately.

eurydice-charis
Download Presentation

Understanding Forces in Fluid Mechanics & Dimensionless Groups

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related