Two liquids of densities $d_{1}, d_{2}$ are mixed with masses in the ratio $3 : 5$ , find density of the mixture.

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Solution

Let the total mass of $d_{1}$ fluid be 3m and the volume is $V_{1}$ .
Let the total mass of $d_{2}$ fluid be 5m and the volume be $V_{2}$ .
So $3 m = d_{1} V_{1}$
$5 m = d_{2} V_{2}$
Now when mixed the total mass $m_{t} = 3 m + 5 m = 8 m$
and total volume is $V = V_{1} + V_{2}$
Density of mixture $d = \frac{t o t a l m a s s}{t o t a l v o l u m e} = \frac{8 m}{V_{1} + V_{2}}$
$d = \frac{8 m}{\frac{3 m}{d_{1}} + \frac{5 m}{d_{2}}}$
$d = \frac{8 d_{1} d_{2}}{3 d_{2} + 5 d_{1}}$

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Two liquids of densities d1,d2 are mixed with masses in the ratio 3:5, find density of the mixture.

Let the total mass of d1 fluid be 3m and the volume is V1.Let the total mass of d2 fluid be 5m and the volume be V2.So 3m=d1V1 5m=d2V2Now when mixed the total mass mt=3m+5m=8mand total volume is V=V1+V2Density of mixture d=totalmasstotalvolume=8mV1+V2d=8m3md1+5md2d=8d1d23d2+5d1

Two liquids of densities $d_{1}, d_{2}$ are mixed with masses in the ratio $3 : 5$ , find density of the mixture.