THERMO- AN D FLUID MECHANICS LECTURE ÓBUDA UNIVERSITY THERMO- AN D FLUID MECHANICS LECTURE Only using inside Dr. Ferenc Szlivka professor Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. Hydrostatic 2. chapter Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Pressure Affect in a point Fig. 2.1 -The pressure is the same from every direction See the figure -The pressure, the force from the pressure is perpendicular to the solid wall Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Equilibrium in a static fluid Fig. 2.4 Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Pressure gradient vector Fig. 2.2 Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Hydrostatic equilibrium in gravitation field Ha Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. Solution of a Hydrostatic problem 1. Choose a proper coordinate system, in which we can write the potential function 2. Choose appropriate points (at least two). In one every parameter is known, in the other we seek an unknown parameter e.g. the pressure 3. Write the potential function 4. Using the equation, where the density is constant, or using the equation, where the density is not constant. In these case we should know an other equation to calculate the density, for example the ideal gas state equation Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. U-tube like a manometer Calculate the pressure difference between the two reservoirs ? Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. Express the pressure differences from the three equations Add the three equations, and so we can find the pressure difference p1-p2 p2 is bigger than p1, so the positive difference is . Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Pressure change in atmosphere Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. The pressure of air Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Temperature exchange in height Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Isothermal atmosphere Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Changing temperature atmosphere Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Polytrophic atmosphere Dr. Szlivka: Thermo- and Fluid Mechanics 2.

a./ Calculate the magnitude of pressure 10 km height ! Calculate the pressure exchange function in trophosphere with different mathematical models ! a./ Calculate the magnitude of pressure 10 km height ! Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Pressure exchange with different mathematical models Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Absolute and gauge pressure Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Forces acting on Hoover-dam Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Tank acceleration in horizontal Áaésé A car with a water reservoir accelerate horizontal with 3 m/s. Te reservoir is 3 m long and height of the water in it is 1.5 m, when the car is in rest. Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. Questions: a./ Calculate the „a" degree ! b./ How much is the maximal gauge pressure on the bottom of the tank? c./ How much is the minimum pressure on the bottom? Solution: Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. Solution: a./ The result force is the vector sum of gravitation acceleration vector plus the opposite vector of the acceleration. The water level is perpendicular to these result vector. b./ The maximum pressure is in the point „A" on the bottom. Write the hydrostatic equation between point "0" and point „A" From these expression we can get the pressure difference between point A and 0: Áaésé . Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. Solution: c./ The minimum pressure is in the point "C" on the bottom. Write the hydrostatic equation between point "0" and point "C" From these expression we can get the pressure difference between point 0 and C: Áaésé . Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Water in rotating tank Fig. 2.15 The tank is rotating around a vertical axes. We are rotating together with the tank, so the water seems to be rest in this coordinate system. The centripetal force acting in the rotating system, which vector is directed from the center out. This centrifugal force has a potential function. Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. Data: Questions: a./ How big is the angular velocity when the water level reaches the top rim of the vessel? b./ What is the function z1=z1(w) when the water level cutting the top of the vessel? c./ Let be the . How much is the pressure difference between the point A and the ambient pressure p0? d./ How much forces acting on the top of the vessel? e./ How much forces acting on the bottom of the vessel? Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. a./ The potential function is the sum of the gravitation and the rotating components, so Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. b./ When the water level is touching the top rim of the vessel. Áaésé Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. c./ When the water level is cutting the top of the vessel. Áaésé Dr. Szlivka: Thermo- and Fluid Mechanics 2.

Dr. Szlivka: Thermo- and Fluid Mechanics 2. c./ The pressure difference between point „A” end the ambient pressure. Áaésé Dr. Szlivka: Thermo- and Fluid Mechanics 2.