Respuesta :

fichoh

Using the principle of dimensional analysis, the representation of Pressure would be [tex] P = F^{1}V^{-\frac{2}{3}}D^{0}[/tex]

Pressure is related to Force, Volume and Density thus :

[tex] Pressure, P = F^{a}V^{b}D^{c}[/tex]

Using dimensional analysis :

  • Pressure, P = ML¯¹T¯²

Substituting the dimension into the relation :

[tex] ML^{-1}T^{-2}= [MLT¯²]^{a} [L³]^{b} [ML¯³]^{c} [/tex]

[tex] ML^{-1}T^{-2} = M^{a+c}L^{a+3b-3c}T^{-2a} [/tex]

Equating the power ;

a + c = 1 - - - (1)

a + 3b - 3c = - 1 - - - (2)

-2a = - 2

a = - 2/-2

a = 1

From (1)

1 + c = 1

c = 1 - 1 = 0

c = 0

From (2) :

1 + 3b - 3(0) = - 1

1 + 3b = - 1

3b = - 2

b = - 2/3

Hence, [tex] P = F^{1}V^{-\frac{2}{3}}D^{0}[/tex]

Learn more :https://brainly.com/question/25690057

raphealnwobi

The representation of pressure is:

[tex]P=FV^{-\frac{2}{3} }[/tex]

Given that:

Force F, volume V and density D are taken as fundamental quantities, hence pressure P is:

[tex]P=F^aV^bD^c\\\\(ML^{-1}T^{-2})=(MLT^{-2})^a(L^3)^b(ML^{-3})^c\\\\\\(ML^{-1}T^{-2})=(M)^{a+c}(L)^{a+3b-3c}(T)^{-2a}[/tex]

Hence:-

2 = -2a

a = 1

a + c = 1

1 + c = 1

c = 0

a + 3b - 3c = -1

1 + 3b - 3(0) = -1

3b = -2b = -2/3

Hence the representation of pressure is:

[tex]P=FV^{\frac{-2}{3} }D^{0}\\\\P=FV^{\frac{-2}{3} }[/tex]

Find out more at: https://brainly.com/question/24894056

Otras preguntas