Fluids: distinguish pressure from force
Work through depth pressure, surface pressure, hydraulic force and displaced volume. Full examples and score limits, without a job or ability band.
This public guide explains one ideal-mechanics topic. Every completed attempt includes all five guides, alongside its correct count and five topic counts. It is not a personal attempt, performance band, percentile or occupational qualification.
Identify the pressure quantity
The fluid questions distinguish a pressure increase due to a stationary liquid column from absolute pressure that also includes the surface value. For a constant-density stationary liquid under the stated gravity, the increase is density times gravitational acceleration times vertical depth. Depth means a vertical separation, not the length of a sloping pipe or the distance around a vessel. Equal-depth comparisons also require attention to which liquid and surface pressure are being held the same. Begin by naming the requested quantity and its unit.
A fresh depth example includes the surface
Suppose liquid density is 950 kg/m³, gravity is 10 N/kg and the point is 0.80 m below the surface. The fluid-column increase is 950 × 10 × 0.80 = 7600 Pa. If the stated surface pressure is 100000 Pa, absolute pressure is 107600 Pa. Without that surface value, the increment can still be calculated but the absolute number is not determined by depth alone. Ratios of column increments therefore cannot automatically be reused as ratios of absolute pressures.
Pascal’s principle transmits a change
In an ideal confined hydraulic system, an added pressure is transmitted through the fluid. For pistons at the same height with the stated losses and weights neglected, equal added pressure means added force divided by piston area is equal. It does not mean every piston receives the same added force. A larger piston area produces a proportionally larger force for that pressure change. Keep the word added visible when surface loads or existing pressure could otherwise be confused with the particular change being calculated.
A fresh hydraulic example checks travel too
Take piston areas of 4 cm² and 20 cm² and an added 18 N force on the small one. The ideal large-piston added force is 18 × 20/4 = 90 N. If an incompressible, leak-free system moves the small piston 6 cm, equal displaced volumes make the large travel 4 × 6/20 = 1.2 cm. Input work is 18 × 0.06 = 1.08 J and output work is 90 × 0.012 = 1.08 J. Force advantage is exchanged for travel.
Read the six answers with the explanations
The six fluid items sample the explicitly stated hydrostatic and ideal hydraulic relations. Their count is not a general fluid-mechanics grade, a percentile or evidence of work with pumps or pressure equipment. A miss may come from an area ratio, an absolute-versus-added distinction or a unit conversion. The report does not infer that cause from the count alone. It shows the actual item answer and reasoning, while all five full guides remain available even when no item was answered correctly.
Check dimensions and fixed conditions
For force from pressure, multiply pressure by area; for pressure from force, divide force by area. An area ratio may use matching cm² units, but a pressure calculation in pascals needs square metres. For a volume relation, pair every piston area with its own displacement. When making a new paper question, explicitly fix density, gravity, surface pressure, relative height and compressibility where needed. These conditions make the answer checkable instead of relying on an imagined container or an unstated hydraulic layout.
Ideal static answers have practical limits
The model excludes flow losses, viscosity effects, compressibility or component weight only where the question explicitly makes those assumptions. It does not measure pressure ratings, real seals, dynamic surges or stability, and a correct word-problem answer supplies no real equipment setting. The exercise is untimed and has no norm, hiring cut-off or certification claim. Repeating the bank may improve familiarity with its wording. Use fresh stated examples to check understanding, without interpreting a one-session count as observed workplace performance or a guaranteed training gain.