CIVL2611 Chap.2 Fluid Properties and Hydrostatic Pressure
Fluid Properties and Hydrostatic Pressure
This chapter links fluid properties to physical response, then develops pressure variation in a static fluid. It covers density, specific weight, specific gravity, viscosity and pressure references before treating manometers as signed elevation paths. The central habit is to move down by adding pressure and move up by subtracting pressure, changing density at every interface.
Density connects mass with volume, specific weight adds gravity, and specific gravity compares density with a reference without carrying units. Viscosity describes shear response rather than static pressure, so it must not be inserted merely because it appears in a data list. The Newtonian plot distinguishes constant proportionality from shear-thinning and shear-thickening behaviour.
Hydrostatics begins from a vertical force balance and shows why pressure depends on elevation change rather than tank shape or sloping path length. Gauge pressure uses atmosphere as zero, while absolute pressure uses a vacuum; both require a clearly stated reference. Multi-fluid manometers are solved as one continuous signed route across interfaces instead of through a memorised device formula.
Original examples include an oil tank, a water-mercury path, a sealed surface and a pressure-depth comparison. Each result is tested against the heavy-fluid column, an approximate ten kilopascals per metre water scale, and the expectation that deeper points carry larger pressure in a connected static liquid.
What this chapter covers
- 01
Density, specific weight and specific gravity
- 02
Newtonian and non-Newtonian viscosity
- 03
Temperature dependence of properties
- 04
Hydrostatic pressure variation
- 05
Gauge and absolute pressure references
- 06
Multi-fluid manometer paths
Worked example · free
Pressure at the base of an oil tank
- +1Set gauge pressure to zero at the exposed surface.
- +1Compute density times gravity times depth to obtain 26.7 kilopascals gauge.
- +1Add atmospheric pressure once to obtain 128.0 kilopascals absolute.
- +1Label both reported pressure references.
Key terms
- Dynamic viscosity
- The Newtonian proportionality between shear stress and velocity gradient.
- Specific gravity
- A dimensionless ratio comparing a fluid density with a reference density.
- Gauge pressure
- Pressure measured relative to local atmospheric pressure.
Fluid Properties and Hydrostatic Pressure FAQ
Why does pressure depend on vertical depth?
A static fluid element supports the weight of fluid above it. The balance produces a pressure gradient aligned with gravity, so only the change in vertical elevation enters the hydrostatic increment, not the sloping path length.
When should atmospheric pressure be added?
Add atmospheric pressure once when converting a gauge result to an absolute result. Do not add it between two points already expressed in the same gauge reference, and label the reference on the final answer.
How should I solve a multi-fluid manometer?
Start at a known pressure and trace one continuous path. Add density times gravity times height when moving down, subtract it when moving up, and change density immediately after crossing an interface.
Exam move
Sketch every fluid interface and draw an arrow along the pressure path. Put a plus or minus sign beside each vertical move before inserting values. Build property flashcards as linked definitions rather than isolated symbols: density connects mass and volume, specific weight adds gravity, specific gravity removes units by comparison, and kinematic viscosity divides dynamic viscosity by density.
On the reverse side, write the units and the physical response each property represents. Add the expected temperature trend for liquid and gas viscosity, but keep the selected tabulated value tied to its actual state. For hydrostatics, practise writing dp/dz with the upward-positive sign, then integrate it for a constant-density liquid.
Use that derivation to explain why tank shape and sloping path length do not change pressure at a fixed vertical depth. Alternate between gauge and absolute questions. Mark the pressure reference before computing, and add atmosphere only when converting the final reference. For manometers, refuse to memorise a special U-tube formula.
Start at a known endpoint, cross each interface once and write a short pressure label after every vertical move. Include examples with water, oil and mercury so the density changes are visually obvious. Compare the final pressure ordering with the heavy-fluid column so the picture independently checks the arithmetic.
Practise one inverse problem in which the pressure difference is given and an interface height is unknown; the same signed path then becomes an equation for geometry. After solving, verify that each term has pressure units and that horizontal moves contributed nothing. Finish a revision set by drawing a pressure-depth plot from a boundary condition.
Show how a denser fluid changes slope and how a pressurised surface shifts the intercept. Those two graph changes provide a fast conceptual check before any numerical answer is trusted. Finish by inventing a three-segment pressure path and asking a study partner to verify only the signs before either of you calculates its value. Verify the chosen pressure reference.