Fluid Dynamics of Fires

Running Head : FLUID DYNAMICS OF FIRES

Fluid Dynamics of Fires

Name

Institution

1 . Classical Mechanics of Fluids

a . From the definition of pressure

, it can be expressed as ,

F /A where F is the applied force and A is the cross sectional area of the surface of the material . Since the hydraulic cylinder has two radial cylinders the pressure at each cylinder can be expressed as taking the subscripts 1 2 to represent the cylinders , then at the smaller cylinder 1 ,

F1 /A1 and at larger cylinders

2 ,

F2 /A2 . But A1 ?R12 and A2 ?R22 . From the law governing pressure in fluids , pressure at both cylinders is equal hence F1 /A1 F2 /A2 . Thus force one can be represented in terms of force two as F1 F2 A1 /A2 . Substituting the area , then

F1 F2 ?R12 ?R22 . This implies that , F1 F2R12 /R22 . And thus the force is

F1 6 .25x103 x9 .81 /1004 61 .3125 N

b . The variation of pressure

, in static liquids is known to depend upon the acceleration due to gravity g , the density of the liquid r , and the elevation z . Use dimensional analysis to determine the hydrostatic law of pressure

Solution

Directional breakdown can be affirmed as , [P] ML-1T-2 (I ?] respectively in dimensional analysis . In dimensional analysis , all these are directly proportional to the force using ? and , that is applying this to equation (I ) above yields

[P] [ ?] ? [g] ? [z] (II

But g L /T2 , [ ?] M /L3 and [z] L . Inserting these into equation two above , I get

M /L T2 (M /L3 (L /T2 (L . This when put in the form of equation (II becomes

ML-1 T-2 (ML-3 (LT-2 (L M ? L -3 (III . this means that the coefficients of M , L and T can be separated and equated with the ones on the opposite side of the equation . That is

For T -2 -2 , for M 1 and for L : -3 -1 (IV

Solving for equation (IV ) above yields 1 from T 1 from M and putting these values into L yields -3 1 -1 , and therefore 1

Having solved for ? and , equation (II ) can then be represented as

P ? g ? z (v

the final equation of hydrostatic law of pressure by dimensional analysis (Vladimir , 2001 ,

. 57

1 .2 . b ) The power law of whirls dissipation in uniform turbulence

Solution

Turbulence or turbulent flow in a fluid system is characterized by disly changes resulting in fast deviations in pressure and velocity . This causes the swirling and turn around effect when a fluid flows past a barrier . This fluid in motion makes a space that is without a fluid flowing on the side of the downstream of the barrier . The fluid which is left behind the barrier flows into the null region making the eddy creation on the edges of the barrier possible . These eddies formed vary in their power , span and energies . As eddies are created , they contain a lot of...