rvanveshana.com
t = 0.00s
Pโ‚Pโ‚‚

Live Telemetry & Summary

Observe the speed and pressure difference. Narrow sections have higher speed and lower static pressure.

Inlet Velocity (vโ‚):2 m/s
Inlet Pressure (Pโ‚):200 kPa
Throat Velocity (vโ‚‚):6.00 m/s
Throat Pressure (Pโ‚‚):184.0 kPa
Pressure Drop (ฮ”P):16.0 kPa

Variable Adjuster

Inlet Area (Aโ‚)60cmยฒ
4080
Throat Area (Aโ‚‚)20cmยฒ
1035
Inlet Velocity (vโ‚)2m/s
15
Inlet Pressure (Pโ‚)200kPa
100300

Bernoulli Fluid Flow Lab

FLOW

The Equation of Continuity states that for an incompressible fluid, mass flow rate is conserved. When fluid flows from a wide inlet (Aโ‚) into a narrow throat (Aโ‚‚), its velocity must increase. Bernoulli's Principle states that an increase in fluid speed occurs simultaneously with a decrease in static pressure (conservation of energy).

A1v1=A2v2,P1+12ฯv12=P2+12ฯv22A_1 v_1 = A_2 v_2, \quad P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2

Whiteboard Solver Steps

Step 1

Conservation of Mass (Equation of Continuity)

For incompressible fluids, the flow rate remains constant. A narrow section forces the fluid particles to speed up.

v2=v1โ‹…A1A2=2โ‹…6020=6.00 m/sv_2 = v_1 \cdot \frac{A_1}{A_2} = 2 \cdot \frac{60}{20} = 6.00 \text{ m/s}
Step 2

Bernoulli's Conservation of Energy

As fluid velocity increases in the narrow channel, the kinetic energy density rises. To conserve total energy, the static fluid pressure must drop.

P2=P1+12ฯ(v12โˆ’v22)=200โ‹…103+500โ‹…(22โˆ’6.002)=184000 PaP_2 = P_1 + \frac{1}{2} \rho (v_1^2 - v_2^2) = 200 \cdot 10^3 + 500 \cdot (2^2 - 6.00^2) = 184000 \text{ Pa}