ENGG2500 Chap.1 Fluid Properties and Hydrostatic Pressure
Fluid Properties and Hydrostatic Pressure
Fluid properties decide which physical effects belong in a model. Density controls mass and weight, viscosity links shear stress to velocity gradient, and pressure acts normally on a surface. Hydrostatics then balances pressure gradients against gravity. The practical method is to choose a pressure reference, trace vertical movement through each fluid, preserve signs and distinguish gauge from absolute pressure.
The chapter also separates dynamic from kinematic viscosity, uses specific gravity as a density ratio and explains why a Mach-number comparison is needed before a gas is treated as incompressible. Every equation is paired with a unit and physical-direction check.
What this chapter covers
- 01
Fluid versus solid response to shear
- 02
Density, specific gravity and viscosity
- 03
Gauge and absolute pressure
- 04
Hydrostatic pressure gradients
- 05
Compound manometer paths
- 06
Compressibility and Mach number
Worked example · free
Pressure below an open water surface
- 1Set free-surface gauge pressure to zero. The mark allocation shown here is not an official assessment scheme.
- 1Compute rho g h = 23.5 kPa.
- 1Add 101 kPa atmosphere for 124.5 kPa absolute.
- 1Check that pressure rises with depth.
Key terms
- Density
- Density is mass per unit volume.
- Dynamic viscosity
- Dynamic viscosity relates Newtonian shear stress to velocity gradient.
- Gauge pressure
- Gauge pressure uses local atmospheric pressure as zero.
- Specific gravity
- Specific gravity is a dimensionless density ratio.
Fluid Properties and Hydrostatic Pressure FAQ
Why does static pressure depend on depth?
A deeper point must support a taller column of fluid above it. Vertical force balance therefore makes pressure increase with downward depth at a rate set by density and gravity. Vessel width and shape do not enter when the fluid is connected and at rest.
How do I choose signs in a manometer?
Start from a point with known pressure and walk through the connected fluids. Moving downward adds density times gravity times vertical distance; moving upward subtracts it. Change density only at an interface, and remember that a horizontal move in one static fluid changes no pressure.
When must I use absolute pressure?
Use absolute pressure when comparing with a physical zero such as vapour pressure or when a gas relation requires it. Gauge pressure is convenient when the same atmospheric pressure surrounds the system and cancels, but the two references must never be mixed in one calculation.
How are dynamic and kinematic viscosity different?
Dynamic viscosity directly relates Newtonian shear stress to velocity gradient and has units of pressure times time. Kinematic viscosity is dynamic viscosity divided by density, so it measures viscous diffusion relative to inertia. Reynolds-number formulas often use kinematic viscosity, while wall-shear relations usually begin with dynamic viscosity.
Why does vessel shape not change hydrostatic pressure?
Pressure difference in one connected resting fluid depends on density, gravity and vertical elevation difference. Sidewall shape changes the wall forces needed to hold the fluid, but it does not change pressure at a given elevation. This is why narrow and wide vessels can share the same bottom pressure at equal depth.
What should I check after a compound-manometer calculation?
Confirm that the denser fluid creates a steeper pressure change, that moving down increased pressure and moving up reduced it, and that the result has pressure units. Then compare the sign with the expected high-pressure side. A path that returns to its starting point must have zero net pressure change.
When is an incompressible model reasonable?
For liquids, density change is often negligible over ordinary engineering pressure ranges. For gases, compare the flow speed with sound speed and consider the pressure variation. A small Mach number supports an incompressible approximation, but the assumption still belongs in the solution because rapid or strongly pressurised gas flow can violate it.
How can units distinguish pressure from shear behaviour?
Pressure and shear stress both have force-per-area units, but viscosity introduces a time scale because it multiplies a velocity gradient. Expand every proposed relation into base units before substitution. If a viscosity equation produces only pressure without the gradient's inverse-time contribution, a property or derivative has been misplaced.
Exam move
Build a property table that lists symbol, meaning and SI unit for density, dynamic viscosity, kinematic viscosity, pressure and specific gravity. Practise classifying a statement by mechanism before choosing an equation: mass and weight point to density, shear points to viscosity, and normal loading points to pressure.
For hydrostatics, draw the free surface and every fluid interface, mark one known pressure and walk to the unknown with one signed term per vertical segment. Keep calculations in pascals until the final conversion. After solving, state gauge or absolute reference, verify that deeper points in the same liquid have higher pressure and check whether the magnitude is plausible compared with one atmosphere.
Rework one compound manometer in the reverse direction to prove the path gives the same pressure difference. Finish with a short gas-flow example in which Mach number decides whether density variation can be ignored.