# Bernoulli Equation

__The Bernoulli Equation:-__

**is basically conservation of energy along a pipe. It can be written in different ways by converting energy to head (Kinsky) or pressure, etc.**

**Bernoulli's equation says in an ideal situation, the TOTAL HEAD = constant.**

**There are assumptions; An ideal fluid (no friction) flowing steadily:-**

**The fluid is incompressible and nonviscous.****There is no energy loss due to friction between the fluid and the wall of the pipe.****There is no heat energy transferred across the boundaries of the pipe to the fluid as either a heat gain or loss.****There are no pumps in the section of pipe under consideration.****The fluid flow is laminar and steady state.**

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__PRESSURE DENSITY__ :-

**Pressure in a fluid is like the energy per unit volume (energy density). From the definition of pressure:**

**Here is the Bernoulli equation in terms of energy per unit volume;**

**Note that this correponds exactly with the conservation of energy equation. Where pressure = spring energy, velocity = kinetic energy and height = potential energy.**

**SE**

Where: PE

_{1}+ KE_{1}+ PE_{1}= SE_{2}+ KE_{2}+ PE_{2}Where: PE

_{1}= mgh_{1}and KE_{1}= 0.5mv_{1}^{2}and SE_{1}= 0.5kx_{1}^{2}

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__TOTAL HEAD:-__

**Total Head (also called Total Dynamic Head) is the sum of the three components; pressure head, velocity head and potential head. From the above equation, divide by**

_{}g. Head is a simple way to think of each term (pressure, velocity and height) in terms of the number of METRES of that fluid it is equivalent to.

**All terms are head (m), which is measured in the working fluid.****You can use gauge or absolute pressure throughout, but gauge is normal****Continuity equation is also true (and often needed to solve the question)****Ideal fluid is assumed (no friction)**

**Bernouli's Equation requires velocity. This is usually found using the continuity equation.**

**= V / t = A**

**Since most pipes are round, this gives;**

**v**

_{1}d^{2}/4 = v_{2}d^{2}/4**or**

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