Physics · Mechanical Properties Of Fluids · NEET
Low pressure. This confuses many students. When a fluid speeds up, its kinetic energy per unit volume goes up. That extra energy has to come from somewhere, so the pressure energy goes down. So faster flow gives LOWER pressure, and slower flow gives HIGHER pressure. Remember: fast fluid, low pressure.
They are two names for the same idea, but used differently. The principle is the plain-language statement (fast flow means low pressure). The equation is the exact math form: P + (1/2)rho v squared + rho g h = constant. On this page we focus on the meaning; the full step-by-step derivation is on the next page.
Think of energy accounting. In an ideal fluid the total energy per unit volume is fixed along a streamline. That total is pressure energy P plus kinetic energy (1/2)rho v squared plus potential energy rho g h. If speed v rises, the kinetic term grows, so to keep the sum constant the pressure term P must fall. No energy is created or lost; it just moves between the three accounts.
No. Bernoulli's principle works for any streamline, level or sloped. The full equation keeps the height term rho g h. The pipe being horizontal is just a common special case: then rho g h is the same at both points and cancels, leaving P + (1/2)rho v squared = constant. That is why for a horizontal pipe you can directly say fast means low pressure.
Four conditions: (1) the flow is steady (streamline, not turbulent), (2) the fluid is incompressible (density constant, true for liquids), (3) the fluid is non-viscous (no internal friction, so no energy lost as heat), and (4) you compare two points on the same streamline. If viscosity matters or the flow is turbulent, Bernoulli's simple form does not apply.
Energy. Bernoulli's equation is just the work-energy theorem (conservation of mechanical energy) written for a flowing fluid. Each term is an energy per unit volume: pressure energy, kinetic energy, and potential energy. Because the ideal fluid has no viscosity, no energy leaks away as heat, so the sum stays constant.
The venturi-meter works on:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Along a streamline of a steady, non-viscous, incompressible fluid, the sum of pressure energy, kinetic energy, and potential energy per unit volume stays constant: P + (1/2)rho v squared + rho g h = constant.
P is the pressure energy per unit volume, (1/2)rho v squared is the kinetic energy per unit volume, and rho g h is the potential energy per unit volume. Here rho is density, v is fluid speed, g is 9.8 m/s squared, and h is height.
Blow air fast between two hanging papers and they move together, not apart. The fast air between them has low pressure, so the higher outside pressure pushes them inward. The same idea explains aeroplane lift and how a venturimeter and atomiser work.
It applies to gases only when the speed is low enough that density stays nearly constant (incompressible). For everyday air flows this is a good approximation, so lift on a wing is often explained with Bernoulli. At very high speeds gases compress and the simple form fails.
Real fluids have viscosity - internal friction between layers. This friction turns some mechanical energy into heat, so the sum P + (1/2)rho v squared + rho g h is no longer constant; it drops along the flow. Bernoulli's simple form assumes zero viscosity, so no energy is lost.
