derive multi vars

amnross

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Derive Eq. 7-1 for the average specific gravity.

spec grav avg=(((a*b)(1+r)) / ((r*b)+a))

How in the world do I derive for mult. var. like this one?
 
Derive Eq. 7-1 for the average specific gravity.

spec grav avg=(((a*b)(1+r)) / ((r*b)+a))

How in the world do I derive for mult. var. like this one?

What is that - where is that???
 
Derive Eq. 7-1 for the average specific gravity.

Eq. 7-1: spec grav avg=(((a*b)(1+r)) / ((r*b)+a))

How in the world do I derive for mult. var. like this one?

What are a, b and r?

Please post compplete problem including definitions of variables.
 
The question out of the book is "Derive Eq. 7-1 for the average specific gravity.

Eq. 7-1: Specific Gravity average=((spec. grav. of oxidizer*spec. grav. of fuel)(1+r))/((r*spec grav of fuel)+spec grav of oxidizer)

r=mixture ratio





What are a, b and r?

Please post compplete problem including definitions of variables.
 
The question out of the book is "Derive Eq. 7-1 for the average specific gravity.

Eq. 7-1: Specific Gravity average=((spec. grav. of oxidizer*spec. grav. of fuel)(1+r))/((r*spec grav of fuel)+spec grav of oxidizer)

r=mixture ratio

r=mixture ratio → is the mixture ratio by weight or by volume?
 
r=mixture ratio (mass flow rate of oxidizer to mass flow rate of fuel

Specific Gravity average=((spec. grav. of oxidizer*spec. grav. of fuel)(1+r))/((r*spec grav of fuel)+spec grav of oxidizer)

spec grav avg=(((a*b)(1+r)) / ((r*b)+a))

Let there be

r gm of fuel → volume = r/a cc

1 gm of fuel → volume= 1/b cc

specific gravity of mixture = (weight of the mixture)/(volume of the mixture) = (1 + r)/(r/a + 1/b) = a*b*(1+r)/(r*b + a)

Cannot be simpler than that - basic definitions and algebra. What grade math (or physics) is this?
 
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