Hydraulics Simulations

A collection of interactive 3D visualizations and simulations to help you master concepts in hydraulics.

Properties of Fluids - Theory & Concepts

Fundamental properties of fluids including density, specific weight, specific gravity, viscosity, surface tension, and compressibility.

Fluid Properties Explorer

Fluid Type

Tube Diameter (

d

)2.0 mm

Plate Velocity (

U

)0.50 m/s

Capillary Rise (Surface Tension)

Observe how tube diameter and fluid type affect rise.

14.8 mm

Calculated Rise (

h

)

Shear Stress (Dynamic Viscosity)

Drag a plate over a 5mm gap of fluid.

MOVING PLATE

0.100 Pa

Shear Stress (

\\tau

)

What this teaches

This simulation illustrates fundamental fluid properties: surface tension and dynamic viscosity. Capillary rise shows how surface tension causes fluids to climb inside narrow tubes, while the shear stress visualization demonstrates how viscosity resists fluid deformation under a moving plate.

Try this

Select Water and decrease the Tube Diameter to 0.5mm. Observe the high capillary rise. Then switch to Oil to see the effect of lower surface tension and different specific weight.
Set Plate Velocity to 1.0 m/s. Switch between Water, Oil, and Honey. Notice the dramatic increase in Shear Stress required to move the plate through Honey due to its much higher dynamic viscosity.

Specific Weight (

\\gamma

)

9810 N/m³

Surface Tension (

\\sigma

)

0.0728 N/m

Dynamic Viscosity (

\\mu

)

0.001 Pa·s

Hydrostatics: Pressure & Manometry - Theory & Concepts - Manometer

Fluid pressure concepts, Pascal's Law, pressure variation with depth, and manometers.

U-Tube Manometer Simulator

Manometer Fluid

Height Difference (

h

): 0.20 m

Differential Pressure

0.00 kPa

P = \\gamma h = \\rho g h

Adjust the height difference to see the corresponding pressure. In a real scenario, the pressure difference causes the height change.

Hydrostatics: Forces on Surfaces - Theory & Concepts - Hydrostatic Force

Calculating hydrostatic forces on plane and curved submerged surfaces, including magnitude and location (Center of Pressure).

Hydrostatic Force on a Rectangular Plane

Depth to Top Edge (

h_1

): 2.0 m

Incline Angle (

\\theta

): 90°

Gate Height (

h

): 3.0 m

Gate Width (

b

): 2.0 m

Total Force (F):0.0 kN

Centroid Depth (

\\bar{h}

):0.00 m

Centroid Distance (

\\bar{y}

):0.00 m

Center of Pressure (

y_p

):0.00 m

Notice that the Center of Pressure ( $y_p$ ), red dot) is always slightly deeper than the Centroid ( $\\bar{y}$ ), blue dot). This eccentricity decreases as the depth increases.

What this teaches

This simulation demonstrates how the magnitude and location of hydrostatic force on a submerged plane surface vary with depth and inclination angle. It highlights the distinction between the centroid (geometric center) and the center of pressure (point of force application).

Try this

Set the Incline Angle to 90° (vertical). Increase the depth from 0m to 5m. Notice how the center of pressure (red dot) gets closer to the centroid (blue dot) as depth increases, but is always below it.
Change the angle to 30°. Observe how the total force decreases compared to 90° at the same depth, due to a lower vertical depth to the centroid.

Relative Equilibrium of Liquids - Theory & Concepts

Analysis of fluids subjected to uniform linear acceleration and rotation, where fluid particles remain at rest relative to the container.

Fluid Dynamics: Energy & Momentum - Theory & Concepts - Bernoulli

Dynamics of fluid flow including Bernoulli's equation, energy lines, the impulse-momentum principle, and practical applications.

Bernoulli's Principle (Venturi Meter)

Inlet Diameter (

D_1

): 200 mm

Throat Diameter (

D_2

): 100 mm

Inlet Velocity (

V_1

): 2 m/s

Inlet (1)

150.0 kPa

2.00 m/s

Throat (2)

0.0 kPa

0.00 m/s

As the area decreases at the throat, velocity must increase (Continuity). This increase in kinetic energy causes a drop in pressure potential energy (Bernoulli). If pressure drops below vapor pressure, cavitation occurs.

Flow in Pipes: Fundamentals & Losses - Theory & Concepts - Reynolds Number

Laminar and turbulent flow, Reynolds number, friction factor, and calculation of head loss in pipes.

Reynolds Number Visualizer

Velocity (

V

): 0.50 m/s

Pipe Diameter (

D

): 0.100 m

Fluid Kinematic Viscosity (

\\nu

): 1.00e-6 m²/s

Calculated Reynolds Number (

Re

)

50,000

Flow Regime: Turbulent

Particle visualization of flow lines. Note: visual speed is scaled.

Flow in Pipes: Fundamentals & Losses - Theory & Concepts - Moody Chart

Laminar and turbulent flow, Reynolds number, friction factor, and calculation of head loss in pipes.

Flow in Pipes: Systems & Networks - Theory & Concepts - Pipe Network

Analysis of complex pipe systems including series, parallel, branching pipes, and networks.

Pipe Systems Calculator

Series ConfigurationParallel Configuration

Total Inflow (

Q

): 100 L/s

Pipe 1

Diameter (mm)150

Length (m)100

Friction factor (f)0.020

Pipe 2

Diameter (mm)150

Length (m)100

Friction factor (f)0.020

Results

Pipe 1 Flow (

Q_1

)0.0 L/s

Pipe 2 Flow (

Q_2

)0.0 L/s

Head Loss Pipe 10.00 m

Head Loss Pipe 20.00 m

TOTAL SYSTEM HEAD LOSS0.00 m

In Parallel, total discharge splits ( $Q = Q_1 + Q_2$ ). The flow divides such that the head loss across each branch is identical: $h_1 = h_2$ .

Flow in Pipes: Systems & Networks - Theory & Concepts - Water Hammer

Analysis of complex pipe systems including series, parallel, branching pipes, and networks.

Water Hammer Simulator

Initial Velocity ($V_0$): 2.0 m/s

Valve Closure Time ($T$): 0.00 s

Critical Time ($T_c$): 0.149s. (If $T \le T_c$, closure is "rapid".)

Pipe Length ($L$): 100 m

Calculated Results

Wave Celerity ($c$):1343 m/s

Critical Time ($T_c$):0.149 s

Max Pressure Surge ($\Delta P$):2.69 MPa

Note: 1 MPa $\approx$ 10.2 meters of water head.

Normal Flow High Pressure Wave Low Pressure Wave

Flow Measurement - Theory & Concepts

Devices and methods for measuring flow rate, including orifices, venturi meters, and weirs.

Open Channel Flow: Uniform Flow - Theory & Concepts

Flow in open channels, geometric elements, Chezy and Manning formulas, and most efficient hydraulic sections.

Open Channel Flow (Manning's Equation)

Discharge (Q)10.0 m³/s

Channel Slope (S)0.0010

Manning's n0.015

Bottom Width (b)2.0 m

Normal Depth (y_n) = 0.000 m

Q = \\frac{1}{n} A R^{2/3} S^{1/2}

Adjust the parameters to see how they affect the normal depth required to convey the given discharge.

Open Channel Flow: Non-Uniform Flow - Theory & Concepts - Specific Energy

Specific energy, critical depth, hydraulic jumps, and gradually varied flow profiles.

Specific Energy Curve ( $E$ vs $y$ )

Discharge (

Q

): 10 m³/s

Channel Width (

b

): 4 m

Unit Discharge (

q=Q/b

):2.50 m²/s

Critical Depth (

y_c

):0.860 m

Min Specific Energy (

E_{min}

):1.291 m

Hover over graph to inspect

The Specific Energy curve shows two possible depths for a given energy $E > E_{min}$ : a subcritical depth (slow, deep) and a supercritical depth (fast, shallow). $y_c$ represents the transition point.

Open Channel Flow: Non-Uniform Flow - Theory & Concepts - Hydraulic Jump

Specific energy, critical depth, hydraulic jumps, and gradually varied flow profiles.

Hydraulic Jump Simulator

Input Parameters

Unit Discharge (q)
Volumetric flow per meter width5.0 m²/s

Upstream Depth (y₁)0.50 m

Note: A jump only forms if the upstream flow is supercritical ( $Fr_1 > 1$ ).

Flow Characteristics

Upstream Froude (Fr₁)

0.00

Supercritical

Sequent Depth (

y_2

)

0.00 m

Downstream Froude (Fr₂)

0.00

Subcritical

Energy Loss (ΔE)

0.00 m

ℹ️ Understanding the Hydraulic Jump

A hydraulic jump occurs when a high-velocity, supercritical flow ( $Fr > 1$ ) transitions into a low-velocity, subcritical flow ( $Fr < 1$ ). This abrupt transition causes a sudden rise in water surface elevation and creates significant turbulence.

Engineers use this phenomenon to intentionally dissipate kinetic energy at the base of spillways and dams, preventing downstream erosion. The conjugate depth equation is used to predict the downstream depth ( $y_2$ ) given the upstream conditions.

Hydraulic Machinery - Theory & Concepts - Pump Characteristics

Principles of pumps and turbines, power calculations, characteristic curves, and cavitation.

Hydraulics Simulations

Properties of Fluids - Theory & Concepts

Fluid Properties Explorer

Capillary Rise (Surface Tension)

Shear Stress (Dynamic Viscosity)

What this teaches

Try this

Hydrostatics: Pressure & Manometry - Theory & Concepts - Manometer

U-Tube Manometer Simulator

Hydrostatics: Forces on Surfaces - Theory & Concepts - Hydrostatic Force

Hydrostatic Force on a Rectangular Plane

What this teaches

Try this

Relative Equilibrium of Liquids - Theory & Concepts

Fluid Dynamics: Energy & Momentum - Theory & Concepts - Bernoulli

Bernoulli's Principle (Venturi Meter)

Flow in Pipes: Fundamentals & Losses - Theory & Concepts - Reynolds Number

Reynolds Number Visualizer

Flow in Pipes: Fundamentals & Losses - Theory & Concepts - Moody Chart

Flow in Pipes: Systems & Networks - Theory & Concepts - Pipe Network

Pipe Systems Calculator

Pipe 1

Pipe 2

Results

Flow in Pipes: Systems & Networks - Theory & Concepts - Water Hammer

Water Hammer Simulator

Calculated Results

Flow Measurement - Theory & Concepts

Open Channel Flow: Uniform Flow - Theory & Concepts

Open Channel Flow (Manning's Equation)

Normal Depth (y_n) = 0.000 m

Open Channel Flow: Non-Uniform Flow - Theory & Concepts - Specific Energy

Specific Energy Curve (EEE vs yyy)

Open Channel Flow: Non-Uniform Flow - Theory & Concepts - Hydraulic Jump

Hydraulic Jump Simulator

Input Parameters

Flow Characteristics

ℹ️ Understanding the Hydraulic Jump

Hydraulic Machinery - Theory & Concepts - Pump Characteristics

Specific Energy Curve ( $E$ vs $y$ )