Heat and Flow Technology I. ÓBUDA UNIVERSITY Heat and Flow Technology I. Use only inside Dr. Ferenc Szlivka Professor Dr. Szlivka: Heat and Flow Technology I_2

Hydrostatic 2. chapter

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

Equilibrium in a static fluid Fig. 2.4

Pressure gradient vector Fig. 2.2

Hydrostatic equilibrium in gravitation field Ha

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

U-tube like a manometer Calculate the pressure difference between the two reservoirs ?

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 .

Pressure change in atmosphere

The pressure of air

Temperature exchange in height

Isothermal atmosphere

Changing temperature atmosphere

Polytrophic atmosphere

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 !

Pressure exchange with different mathematical models

Absolute and gauge pressure 2.9 ábra

Forces acting on Hoover-dam Fig. 2.8

Tank acceleration in horizontal Fig. 2.14 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.

Questions: a. / Calculate the „a" degree. b 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:

b./ The maximum pressure is in the point „A" on the bottom. 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 .

c./ The minimum pressure is in the point "C" on the bottom. 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 .

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.

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?

a./ The potential function is the sum of the gravitation and the rotating components, so

b./ When the water level is touching the top rim of the vessel. Áaésé

c./ When the water level is cutting the top of the vessel. Áaésé

c./ The pressure difference between point „A” end the ambient pressure. Áaésé