Hydrostatic Pressure Apparatus Notes

Introduction to Hydrostatic Pressure Apparatus

  • Fluid mechanics combines the laws of statics, dynamics, and thermodynamics.
  • Focuses on fluid behavior treated as continuous media.
  • Key laws: Conservation of mass, energy, and momentum.
  • Purpose of F1-12 Hydrostatic Pressure Apparatus: Demonstrate hydrostatic pressure principles.

Description of the Apparatus

  • Components:
    • Beam level indicator
    • Quadrant with clamping screw
    • Knife edge pivot
    • Balance arm with counterbalance and balance pan
    • Spirit level for alignment
  • Functionality:
    • Quadrant rotates around pivot to measure hydrostatic forces when immersed.
    • Water levels can be adjusted using a flexible tube.
    • Drain cock facilitates water removal from the tank.

Nomenclature and Variables

  • Key Variables:

    • Height of Quadrant: $D$ (m)
    • Width of Quadrant: $B$ (m)
    • Length of Balance Arm: $L$ (m)
    • Quadrant to Pivot Distance: $H$ (m)
    • Depth of Immersion: $d$ (m)
    • Hydrostatic Thrust: $F = pgA\ h$ (N)
    • Centre of Pressure Depth: $h'$

  • Parameters:

    • Area $A = B imes d$
    • Hydrostatic Thrust for Partially Submerged Body: $F = pgBD(d - D)$
    • Centre of Pressure Depth (
    • Calculations involve experimental and theoretical comparisons and adjustments based on measurements.

Experimental Procedure

Objective
  • Determine hydrostatic thrust on submerged surface.
  • Compare experimental vs theoretical positions of line of action.
Equipment Needed
  • F1-10 Hydraulics Bench
  • F1-12 Hydrostatic Pressure Apparatus
  • Set of weights
  • Measuring tools (not supplied)
Setup
  1. Level tank using spirit level and adjust until horizontal.
  2. Ensure balance arm is on knife edges and weight hanger in proper location.
  3. Fill tank with water, measuring depth until balance is horizontal after adding specified weights.
Data Collection
  • Record various parameters including mass, depth of water, thrust, and moments involved in the balance.
  • Repeat for different weight increments to ensure reliable experimental outputs.

Processing Results

  • Tabulation of readings on thrusts, depth, and moments to identify accuracy differences between experimental and theoretical data.

Theoretical Considerations

  • Hydrostatic thrust defined for both partially submerged and fully submerged vertical surfaces.
  • Moment equilibrium provides relationship between hydrostatic thrust and applied weight from balance experiments.
  • Key Equations:
    • Moment: (M = Fh'')
    • Equilibrium Condition:
    • (Fh'' = WL = mgL)
    • Theoretical Centre of Pressure:
    • (h' = \dfrac{I}{A h})
    • Adjustment of centre of pressure shifts depending on complete vs partial immersion.

Conclusion Points

  1. Discuss variations in thrust with water depth.
  2. Evaluate depth of the centre of pressure concerning submersion depth.
  3. Analyze discrepancies between theoretical and experimental results.