Respuesta :
Answer:
The volumetric ratio is 0,71
Explanation:
Let's begin with the equation:
[tex]Db = Mb/Vb[/tex] (1)
Where:
Db: Blend Density, Mb: Blend Mass and Vb: Blend Volume
And we know: [tex]Vb = Vg + Vk[/tex] (2)
Where:
Vg: Gasoline Volume and Vk: Kerosene Volume
Therefore replacing (2) into (1):
[tex]Db = (Mg + Mk) / (Vg + Vk)[/tex]
[tex]Db = (Dg * Vg + Dk * Vk)/(Vg + Vk)[/tex] (3)
Where:
Dg: Gasoline Density and Dk: Kerosene Density
The specific gravity is defined as:
[tex]SG = Substance Density / Reference Density[/tex]
Therefore:
[tex]Db = SGb * Dref\\Dg = SGg * Dref\\Dk = SGk * Dref[/tex]
Where:
Dref: Reference Density
SGb: Blend Specific Gravity
SGg: Gasoline Specific Gravity (which is 0.7 approximately)
SGk: Kerosene Specific Gravity
Replacing these equations into (3) we get:
[tex]SGb * Dref = (SGg * Dref * Vg + SGk * Dref * Vk)/(Vg + Vk)[/tex]
[tex]SGb * Dref = Dref * (SGg * Vg + SGk * Vk)/(Vg + Vk)[/tex]
[tex]SGb = (SGg * Vg + SGk * Vk)/(Vg + Vk)[/tex]
[tex]SGb * (Vg + Vk) = SGg * Vg + SGk * Vk[/tex]
[tex]SGb * Vg + SGb* Vk = SGg * Vg + SGk * Vk[/tex]
Replacing with the Specific Gravity data, we obtain:
[tex]0.77 * Vg + 0.77 * Vk = 0.7 * Vg + 0.82 * Vk[/tex]
[tex]0.77 * Vg - 0.7 * Vg = 0.82 * Vk - 0.77 * Vk[/tex]
[tex]0.07 * Vg = 0.05 * Vk[/tex]
[tex]Vg/Vk = 0.05/0.07[/tex]
[tex]Vg/Vk = 0.71[/tex]
