Fluid Pressure Study Notes

  • Fluid Pressure

    • Fluids are materials that can flow and have no definite shape of their own. This includes liquids and gases, which are significant in various physical and engineering applications.

    • Pressure: Defined as the perpendicular component of a force applied to a surface divided by the area of that surface. The formula for pressure is given by:

      P=FAP=AF​
      where:

      • PP is the pressure,

      • FF is the force applied, and

      • AA is the area over which the force is distributed.

    • The unit of pressure is the Pascal (Pa), which is equivalent to one Newton per square meter (N/m²).

    • Pressure is a scalar quantity, meaning it has magnitude but no direction.

  • Pressure Types

    • Absolute Pressure: This is the pressure measured relative to a perfect vacuum (absolute zero pressure). It provides a standard frame of reference for pressure measurement.

    • Gauge Pressure: This is the difference between the absolute pressure and the atmospheric pressure. It indicates how much pressure is measured above or below the current atmospheric pressure. Gauge pressure is commonly used in many industrial applications, such as tire pressure measurements.

  • Pressure Relationships

    • Pressure varies inversely with area, as described by the relationship:

      • A larger area results in smaller pressure for a given force applied. For example, wide tires on a vehicle reduce pressure on the ground to prevent sinking in soft surfaces.

      • Conversely, a smaller area results in larger pressure. A sharp object like a needle can exert high pressure on a surface due to its small area, enabling it to penetrate more easily.

  • Sample Problems

    1. Average pressure exerted by a child and stool:

    • Total weight = 364 N (child) + 41 N (stool) = 405 N

    • Area of stool = 19.3 cm² = 0.00193 m²

    • Using the pressure formula:

    • P=405:N0.00193:m2≈2.1×105:PaP=0.00193:m2405:N​≈2.1×105:Pa

    1. Atmospheric pressure exerted on a desk:

    • Average atmospheric pressure P=1×105:PaP=1×105:Pa

    • Area of the desk = 152 cm x 76 cm = 0.11576 m²

    • Calculating force using the pressure-area relationship:

    • F=P×A=1×105×0.11576≈1.2×105:NF=P×A=1×105×0.11576≈1.2×105:N

  • Typical Pressures

    • Center of Earth: High pressures due to the immense weight of overlying material, approximately 4×108:kPa4×108:kPa

    • Deepest ocean trench (Mariana Trench): Extreme hydrostatic pressure at depths of 11,000 meters, approximately 1.1×105:kPa1.1×105:kPa

    • Standard atmospheric pressure at sea level: 1.01325×102:kPa1.01325×102:kPa, which is the baseline for many other pressure measurements.

  • Pressure Depth Formula

    • The total pressure at a certain depth in a fluid is calculated by the formula:

    P=Patm+PgaugeP=Patm+Pgauge

    where:

    • PatmPatm​ is the atmospheric pressure above the fluid,

    • PgaugePgauge​ is the pressure due to the fluid column.

  • Critical Thinking Example

    • Why is a dam thicker at its base than at its top?

    • Dams are designed to withstand higher pressures from the water above due to the weight of the water. The increased thickness at the base allows the structure to resist hydraulic forces effectively, given that pressure increases with depth in a fluid. This principle is essential for maintaining structural integrity and safety.