≈ Fluidi

Idrostatica e idrodinamica dei fluidi ideali: leggi di Pascal, Stevino, Archimede, Bernoulli e applicazioni.

📋 Formulario

Complete Theory

Worked Examples

Example 1Buoyant force on aluminium cube
Example 2Hydraulic press — lifting a car

Exercises with Solutions

Exercise 1Partially submerged bodyHard
📋 Problem to solve
A block of volume V=2×10−3V=2\times10^{-3} m³ floats on water with 60% of its volume submerged. (a) Determine the density of the block. (b) If an additional mass mp=0.5m_p=0.5 kg is placed on top of the block, what percentage of the volume remains above water?
📌 Given data
V=2×10⁻³ m³60% submerged (initial condition)ρ_H₂O=1000 kg/m³m_p=0.5 kg (added mass)
Exercise 2Torricelli barometerHard
📋 Problem to solve
A mercury barometer reads a height h=762h=762 mm. (a) Calculate the atmospheric pressure in pascals. (b) What height would a water barometer have under the same conditions? (c) On a planet with gp=3.7g_p=3.7 m/s², how many mm of Hg would the same barometer read (same Earth PatmP_{atm})?
📌 Given data
h=0.762 m (Hg column height)ρ_Hg=13600 kg/m³ (mercury density)g=9.81 m/s² (Earth gravity)g_p=3.7 m/s² (planetary gravity)
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Recommended Books

Introductory
Fluid Mechanics
Frank M. White
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Integrative Problems

Problems combining all chapters — exam level
Problem 1The Dam, the Hydraulic Conduit, and the Water JetEXTREME
A dam holds back an artificial lake. The water (ρ=1000 kg/m3\rho = 1000\,\mathrm{kg/m^3}) reaches a height H=30 mH = 30\,\mathrm{m} above the lowest point of the dam. The wall is W=50 mW = 50\,\mathrm{m} wide.

At h1=5 mh_1 = 5\,\mathrm{m} from the bottom there is a valve connected to a conduit that transitions from cross-section A1=0.20 m2A_1 = 0.20\,\mathrm{m^2} to a constriction A2=0.05 m2A_2 = 0.05\,\mathrm{m^2} (Venturi tube), then widens again and terminates at h2=15 mh_2 = 15\,\mathrm{m} with a nozzle of area A3=0.03 m2A_3 = 0.03\,\mathrm{m^2}.
📌 Problem data
H = 30\,\mathrm{m}\;(\text{lake depth})\rho = 1000\,\mathrm{kg/m^3}W = 50\,\mathrm{m}\;(\text{dam width})h_1 = 5\,\mathrm{m}\;(\text{valve elevation})A_1 = 0.20\,\mathrm{m^2},\; A_2 = 0.05\,\mathrm{m^2},\; A_3 = 0.03\,\mathrm{m^2}h_2 = 15\,\mathrm{m}\;(\text{nozzle elevation})
(a)Hydrostatics — Stevin + Total Force(b)Hydrostatics + Torricelli(c)Fluid Dynamics — Bernoulli + Venturi(d)Bernoulli with Elevation — Nozzle at Height(e)Hydraulic Power — Archimedes + Work