Fluid Mechanics: Pressure Concepts

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Questions and Answers

What are the units of pressure in the SI system?

  • kg/m<sup>2</sup> (correct)
  • N/m<sup>2</sup> (correct)
  • kg/s<sup>2</sup>
  • m/s<sup>2</sup>

What is the relationship between absolute pressure (Pabs), gage pressure (Pg), and atmospheric pressure (Patm)?

  • P<sub>abs</sub> = P<sub>g</sub> + P<sub>atm</sub> (correct)
  • P<sub>atm</sub> = P<sub>abs</sub> - P<sub>g</sub>
  • P<sub>atm</sub> = P<sub>g</sub> - P<sub>abs</sub>
  • P<sub>abs</sub> = P<sub>g</sub> - P<sub>atm</sub>

Which of the following units is NOT a common unit for pressure?

  • kg/s (correct)
  • kgf/cm<sup>2</sup>
  • lbf/ft<sup>2</sup>
  • 10<sup>3</sup> Pa

What is the pressure at a point in a stationary fluid called?

<p>Static pressure (B)</p> Signup and view all the answers

What is the relationship between pressure and depth in a fluid?

<p>Pressure increases linearly with depth. (C)</p> Signup and view all the answers

What is the principle that states that pressure at a point in a fluid is the same in all directions?

<p>Pascal's Law (A)</p> Signup and view all the answers

Which equation is obtained from the equilibrium of forces in the x-direction for the differential element in the proof of Pascal's Law?

<p>P<sub>1</sub> △z△y - P<sub>3</sub> △y l sinθ = 0 (B)</p> Signup and view all the answers

A barometer is used to measure:

<p>The atmospheric pressure. (A)</p> Signup and view all the answers

Why is pressure considered a scalar quantity for a stationary fluid?

<p>It only has magnitude and no specific direction. (B)</p> Signup and view all the answers

In a connected fluid under static conditions, the pressure at the same height from the free surface is:

<p>The same, regardless of the type of fluid. (B)</p> Signup and view all the answers

What is the principle behind mechanical advantage, as applied in the context of hydraulic systems?

<p>The pressure remains constant, while force is amplified by a larger area. (B)</p> Signup and view all the answers

What is the value of 1 ban expressed in Pa?

<p>10<sup>5</sup> Pa (C)</p> Signup and view all the answers

In the provided example problem, why is the pressure at point 'c' greater than the pressure at point 'b'?

<p>The pressure at point 'c' is higher due to the weight of both water and oil columns above it. (C)</p> Signup and view all the answers

In the example problem, how is the absolute pressure at point '1' calculated?

<p>By subtracting the sum of pressures due to each fluid column from the atmospheric pressure. (C)</p> Signup and view all the answers

What is the principle behind the formula â–³P = P2 - P1 = - Pg h?

<p>The pressure difference between two points is directly proportional to the density and the height difference. (C)</p> Signup and view all the answers

Flashcards

Variation of Pressure with Depth

Describes how pressure changes with depth in a fluid due to gravity.

Connected Fluid Pressure

Pressure at the same height in connected fluids is equal.

Pressure Absolute Equation

P_abs = P_atm + pgh, relates absolute pressure to atmospheric pressure and fluid height.

Mechanical Advantage

The factor by which a mechanism multiplies the force put into it.

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Barometer

An instrument used to measure atmospheric pressure.

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Manometers

Devices used to measure pressure differences in fluids.

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Layered Liquids Pressure

Pressure in liquids changes based on the density and height of layers.

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Pressure Calculation Example

An example using various fluid densities and heights to find absolute pressure.

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Pressure

Normal force exerted by fluid per unit area.

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Units of Pressure

Pressure measured in Pa (N/m²), MPa, kPa, psi, and kgf/cm².

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Absolute Pressure

Pressure measured with reference to a vacuum.

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Gage Pressure

Pressure measured with reference to atmospheric pressure.

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Pressure at a point

Pressure is the same in all directions in a fluid.

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Pascal's Law

The pressure change at any point in a confined fluid is transmitted undiminished in all directions.

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Pressure Conversion

Conversions between different pressure units (e.g., 1 MPa = 10^6 Pa).

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Density of liquids

Density impacts pressure; more density leads to higher pressure at same depth.

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Study Notes

Pressure

  • Pressure is defined as the normal force exerted by a fluid per unit area.
  • SI unit: Pascal (Pa) = N/m². Common units include MPa and kPa.
  • USCU unit: lbf/ft² Other units include kgf/cm².
  • 1 slug = mass in USCU
  • 1 lbf = 1 lbm x 32.2 ft/s²
  • 1 lbf/in² = 1 psi
  • Conversions between units are included in the document.

Absolute vs. Gauge Pressure

  • Absolute pressure: Pressure relative to a vacuum.
  • Gauge pressure: Pressure relative to atmospheric pressure.
  • Pabs = Pg + Patm

Pressure at a point in a fluid

  • Pressure at a point in a stationary fluid is the same in all directions at that depth.
  • A scalar quantity for a stationary fluid

Proof

  • The sum of forces in any direction is zero.
  • Pressure is the same at a given depth, irrespective of direction.

Layered liquids

  • For layered liquids, pressure at a certain depth is determined by the layers above it.
  • The pressure from each layer is summed at that point.
  • Pressure increases with depth in each layer.

Manometers

  • Manometers measure pressure differences between two points.
  • Pgas = Pabs = Patm + pgh (p = density, g = acceleration due to gravity, h = height of column).
  • A device used to measure pressure
  • Mercury or other liquids used in manometers.

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