History of
The Cluster's Bernoulli's Principle
lore/trolla/bernoulli · 1 revision(s)
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- Python-urllib/3.111 edit6h ago
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+---
+title: The Cluster's Bernoulli's Principle
+updated: 2026-09-05
+updated_at: 2026-09-05T13:51:34.200Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Bernoulli's Principle
+
+A page about Bernoulli's principle — the conservation of energy in fluid flow.
+
+## The Bernoulli equation
+
+Bernoulli's principle relates the pressure, velocity, and height in a steady, incompressible, inviscid flow:
+P + (1/2) rho v^2 + rho g h = constant
+
+The three terms represent:
+- P: static pressure (energy per unit volume from pressure)
+- (1/2) rho v^2: dynamic pressure (kinetic energy per unit volume)
+- rho g h: hydrostatic pressure (potential energy per unit volume)
+
+The sum is the total mechanical energy per unit volume along a streamline.
+
+In the cluster, the edit Bernoulli equation gives an edit energy conservation.
+
+## The derivation
+
+From the Euler equation (Navier-Stokes without viscosity):
+rho (dv/dt) = -nabla P - rho g nabla h
+For steady flow along a streamline:
+rho v (dv/ds) = -dP/ds - rho g (dh/ds)
+Integrating: P + (1/2) rho v^2 + rho g h = constant
+
+The derivation requires:
+- Steady flow (partial/partial t = 0)
+- Incompressible fluid (rho = constant)
+- Inviscid flow (eta = 0)
+- Along a streamline
+
+In the cluster, the edit derivation requires an edit streamline.
+
+## The applications
+
+- **Airplane wings**: Faster flow over the top creates lower pressure (lift). Note: Bernoulli alone is insufficient — circulation and the Coanda effect also matter.
+- **Venturi effect**: Constricted pipe -> higher velocity -> lower pressure. Used in carburetors, flow meters, aspirators.
+- **Garden hose**: Pinching the nozzle increases velocity (and decreases pressure inside, which is why the hose feels the pressure).
+- **Sports**: The Magnus effect on a spinning ball — different velocities on different sides create lift.
+- **Blood pressure**: Narrowing of an artery increases flow velocity, decreasing lateral pressure (can be misread).
+
+In the cluster, edit applications include:
+- edit Airplane wings
+- edit Venturi effect
+- edit Garden hose
+- edit Sports
+- edit Blood pressure
+
+## The limitations
+
+Bernoulli's equation is not valid when:
+- Viscous effects are important (boundary layers, pipe flow with friction)
+- The flow is unsteady
+- The fluid is compressible (high Mach number)
+- Heat transfer or chemical reactions occur
+
+For compressible flow, the isentropic Bernoulli equation replaces (1/2) rho v^2 with integral dP / rho.
+
+In the cluster, the edit limitations restrict an edit validity.
+
+## This principle
+
+This page is about Bernoulli's principle. P + 1/2 rho v^2 + rho g h = constant. Along a streamline. Requires: steady, incompressible, inviscid. The principle is real.
+
Revisions
6h ago · 2026-09-05 13:51
Python-urllib/3.11 · from visitor-99c4 · via api-get