Fluid Dynamic Calculators

Outflow of Fluid From a Vessel

In this calculation, the process of fluid outflow through a hole of diameter D from a reservoir of volume V with a cross-section constant in height and an initial level h is considered.

The amount of fluid dV flown in an infinitely small period of time dt at a conditionally constant flow rate Q is equal to:

dV = Q*dt
dV = μ*(πD² / 4) * (2gh)^1/2*dt

On the other hand of the equation, the amount of flown fluid is equal to:

dV = (V/h) dh

Equating the right-hand sides of the equations, we get:

dt = [(V/h) / μ*(πD² / 4)*(2gh)^1/2] dh

As a result of solving this equation, the time t required for the complete emptying of the tank is determined.

Hydrodynamic of Pipelines

Hydrodynamic of Pipes

INITIAL DATA

h - Initial fluid level;

V - Vessel volume;

D - Hole or nozzle diameter.

Calculation condition:
Vessel cross-section is constant.

RESULTS DATA

t - Time of vessel emptying.

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BASIC FORMULAS

Emptying time:

t = 8V / μ*π*D²*(2gh)^0.5;

μ = 0.62 - flow rate coefficient for the hole;
μ = 0.83 - for nozzle with sharp inlet edge (figure I);
μ = 0.97 - for nozzle with smooth inlet edge (figure II);
μ = 1.15 - for cone nozzle with smooth inlet edge (figure III). Nozzle taper 7°<β<12°.

INITIAL DATA

h - Initial fluid level;

V - Vessel volume;

D - Hole or nozzle diameter.

Calculation condition:
Vessel cross-section is constant.

RESULTS DATA

t - Time of vessel emptying.

OTHER CALCULATORS

AREA MOMENTS OF INERTIA

BEAM CALCULATORS

TORSION OF BARS

CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

SHAFT CONNECTIONS

BEARINGS

DRIVES

FATIGUE

HEAT TRANSFER