Problem 105P

The composition of a liquid with suspended solid particles is generally characterized by the fraction of solid particles either by weight or massCsmass= ms/mm or by volume,Csvol = ˅s/ ˅m wherem is mass and ˅ is volume. The subscriptss and m indicate solid and mixture, respectively. Develop an expression for the specific gravity of a water- based suspension in terms ofCsmass and Cs vol.

Solution to 105P

Step 1

We need to find the expression for specific gravity of water based suspension in terms of CSmass and CsVol. For finding the specific gravity, we will consider the fluid as water.

Mass of the solid suspended in the water=Ms

Volume of the solid suspended in water=Vs

Mass of the water=Mw

Volume of water=Vw

Total mass=Ms+Mw=Mt

Total volume=Vs+Vw=Vt,

Dividing the total volume by Vt

......................................................(1)

Dividing the total mass by Mt

...................................................(2)

ρ=density

V= volume

From equation 1,

Thus we have expressed the specific gravity in terms of the CsVol and CSmass .