Bernoulli’s Principle

Usually, liquids are considered “incompressible”, meaning that the density of the liquid remains nearly constant. Gases are easily compressed, like air in a tire or air compressor. FLUID FLOW CONTINUITY

As a liquid flows from one container to another, the mass of liquid flowing from one section to another is equal, the density is equal, the volume is equal…etc…THEY ARE EQUAL CONT.

Bernoulli’s equation is the conservation of energy applied to a moving fluid. As fluid moves from one chamber to another or from one high to another work is done. BERNOULLI’S EQUATION P 1 +1/2 ρ V ρ gh 1 = P 2 + 1/2 ρ V ρ gh 2 P=pressureg= acceleration due to gravity Ρ =density of the fluidh =is the height of the fluid V = the speed of the fluid BERNOULLI’S EQUATION

CONSIDER THIS A tank filled with fluid, as shown, is open at the top and has a hole in the side. The cylinder is small so the change in height does not cause a great deal of difference in pressure. The speed that the fluid moves in the tank is much smaller than the speed of the fluid coming out of the hole. So much smaller we can consider Vel tank or V 1 =0m/s

Applying these conditions to Bernoulli’s Equation to solve for V 2, we write CONSIDER CONT.

P 1 +1/2 ρ (0) + ρ gh 1 = P 2 +1/2 ρ V ρ gh 2 Subtracting P 1 from both sides: Ρ gh 1 = ½ ρ V ρ gh 2 Divide by ρ on both sides: gh 1 = 1/2V 2 2 +gh 2 Solving for V 2 : V 2 = √ 2g (h 1 -h 2 ) ANSWER

Lets Suppose the Fluid is water … h 1=.06m h 2 =.03m What is the numerical value of V 2 ? EXTENDED

.76m/s ANSWER