≈ Fluids

Hydrostatics and hydrodynamics of ideal fluids: Pascal, Stevin, Archimedes and Bernoulli laws, with applications. Every topic with step-by-step theory, interactive diagrams and solved exercises.

📋 Formulario

Complete Theory

Worked Examples

Example 1Venturi tube — flow rate measurement
Example 2Torricelli's theorem — jet range

Exercises with Solutions

Exercise 1Bernoulli with elevationHard
📋 Problem to solve
Water flows in a horizontal conduit that then rises to z2=3z_2=3 m. In section 1 (elevation z1=0z_1=0): A1=50A_1=50 cm², P1=2×105P_1=2\times10^5 Pa, v1=1.5v_1=1.5 m/s. In section 2: A2=20A_2=20 cm², z2=3z_2=3 m. Find v2v_2 and P2P_2 (water density ρ=1000\rho=1000 kg/m³).
📌 Given data
A_1=50 cm² (section 1)P_1=2×10⁵ Pa (pressure at 1)v_1=1.5 m/s (velocity at 1)A_2=20 cm², z_2=3 m (section 2 and elevation)ρ=1000 kg/m³ (water)
Exercise 2Tank drainingVery Hard
📋 Problem to solve
A cylindrical tank of diameter D=2D=2 m has a hole of diameter d=4d=4 cm located at zhole=0.5z_{hole}=0.5 m from the bottom. The initial water level is H0=4H_0=4 m from the bottom. (a) Calculate the drain time. (b) Determine the initial jet range (consider the hole on the side, at zhole=0.5z_{hole}=0.5 m from the ground).
📌 Given data
D=2 m (tank diameter)d=0.04 m (hole diameter)z_hole=0.5 m (hole height from ground)H_0=4 m (initial water level)
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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 m  (lake depth)H = 30\,\mathrm{m}\;(\text{lake depth})ρ=1000 kg/m3\rho = 1000\,\mathrm{kg/m^3}W=50 m  (dam width)W = 50\,\mathrm{m}\;(\text{dam width})h1=5 m  (valve elevation)h_1 = 5\,\mathrm{m}\;(\text{valve elevation})A1=0.20 m2,  A2=0.05 m2,  A3=0.03 m2A_1 = 0.20\,\mathrm{m^2},\; A_2 = 0.05\,\mathrm{m^2},\; A_3 = 0.03\,\mathrm{m^2}h2=15 m  (nozzle elevation)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