Lecture 14- Hydrostatics (slides)

Fluids

• Definition: Fluids are substances that flow and can be classified as liquids or gases.

Density

• Definition: Density p (in kg/m³) relates the mass and volume of a fluid.

  • Formulae:

  • $m = \rho V$

  • $V = \frac{m}{\rho}$

Pressure

• Definition: Pressure is defined as force per unit area.

  • SI Unit: Pascal (Pa)

    Example Calculation:

  • A student with a mass of 83 kg has sneakers with a total surface area of 0.0290 m².

  • Pressure exerted:
    $P = \frac{F}{A} = \frac{mg}{A}$

Atmospheric Pressure

• Standard Atmospheric Pressure:
  $P_0 = 1 \text{ atm} = 101,325 \text{ Pa}$

Hydrostatic Equation

• Principle:

  • Any pressure applied to a fluid is transmitted equally throughout the fluid as well as the walls of the container (Pascal’s Principle).

  • Hydrostatic Equation:
    $P = P_{atm} + \rho gh$

    • P atm is atmospheric pressure,

    • p is fluid density,

    • g is acceleration due to gravity,

    • h is height or depth in the fluid.

  • Describes how pressure changes with depth in a fluid.

Measuring Pressure

• Absolute Pressure:

  • Measured using a barometer.

  • The formula is:
    $P = P_{0} + \rho g h$ (where ( h ) is the height of the fluid).

  • Can use to calculate the atmospheric pressure if you have height and vice versa.

    

    • In theory it dosen’t have to be mercury used (but for practical reasons it is good to use so the barometers not 10 feet tall)

• Gauge Pressure:

  • Measured using a manometer.

  • Defined relative to atmospheric pressure:

    • Looking at the difference in pressure - relative to atmosphere
      $P{gauge} = P - P{atm}$

      • Where: $P = \frac{F}{A} = \frac{mg}{A}$

        

• Measuring Blood pressure is a example of this.

  • The two numbers you measure (e.g. 120/ 70) represent the systolic and diastolic pressures, respectively, indicating the pressure in the arteries during heartbeats and between beats.

Buoyancy

• Definition: The upward force exerted by a fluid on a submerged object.

• Archimedes' Principle:

  • States the buoyant force is equal to the weight of the fluid displaced by the object:
    $F_B = \rho g V$

Sinking & Floating Objects

• To determine if an object will sink or float:

  • Compare the densities (p) of the object and the fluid.

  

  Example:

  • Iceberg's submerged volume in seawater:

  • Given densities:
    $\rho.{ice}=920\text{ kg/m}^3$ $\rho{w} = 1030 \text{ kg/m}^3$

  • Determine the proportion of the iceberg below water based on these densities.