Fluid Dynamics & Bernoulli Lab

Investigate how pressure, velocity, and height relate in flowing fluids. Apply Bernoulli's equation, the continuity equation, and Torricelli's theorem to real-world scenarios including airplane lift, Venturi meters, and tank drainage.

Guided Experiment: Exploring Continuity

What happens to the velocity of a fluid when the pipe cross-sectional area is reduced by half? How does the flow rate change?

Write your hypothesis in the Lab Report panel, then click Next.

Pipe Flow Diagram

Point 1Point 2P = 200.0 kPav = 2.00 m/sP = 194.0 kPav = 4.00 m/s

Controls

Point 1
Point 2
Fluid Properties

Solution Steps

1Bernoulli's equation
2Substitute known values
3Solve for P₂
4Reynolds number
5Venturi pressure difference
Solved
p2 = 194000
Pa
Flow Rate Q₁
0.02 m³/s
Flow Rate Q₂
0.02 m³/s
Reynolds Number
199601
Turbulent
Venturi ΔP
6000 Pa
Energy Conservation Check
Left total: 202000 Pa
Right total: 202000 Pa
Energy is conserved between both points

Data Table

(0 rows)
#ConfigurationPressure (Pa)Velocity (m/s)Height (m)Area (m²)Flow Rate (m³/s)Reynolds No.
0 / 500
0 / 500
0 / 500

Reference Guide

Bernoulli's Equation

For an ideal, incompressible fluid flowing along a streamline, the total mechanical energy per unit volume is conserved.

P+12ρv2+ρgh=constantP + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}

When pressure energy increases, kinetic energy must decrease (and vice versa). This explains why faster-moving fluids exert less pressure on their surroundings.

Continuity Equation

Mass conservation requires that the flow rate Q stays constant throughout a pipe. When the cross-section narrows, velocity must increase.

A1v1=A2v2Q=Av=constantA_1 v_1 = A_2 v_2 \quad \Rightarrow \quad Q = Av = \text{constant}

This is why covering part of a garden hose nozzle makes the water spray farther.

Torricelli's Theorem

The speed of fluid draining from a hole at the bottom of a tank depends only on the height of fluid above the hole, not on the tank size.

v=2ghv = \sqrt{2gh}

This is a special case of Bernoulli's equation where both surfaces are at atmospheric pressure and the tank surface velocity is approximately zero.

Reynolds Number

The Reynolds number predicts whether flow will be smooth (laminar) or chaotic (turbulent). It compares inertial forces to viscous forces.

Re=ρvDμ\mathrm{Re} = \frac{\rho v D}{\mu}

Re < 2300 is laminar, 2300-4000 is transitional, and Re > 4000 is turbulent. Most everyday pipe flows are turbulent.