Answer to Question #234066 in Mechanical Engineering for Randal Rodriguez

Question

2. Two liquids of different densities (ρ 1 = 1550 kg m /m 3 and ρ 2 = 550 kg m /m 3 ) are poured together in a

cylindrical container 0.5 m in diameter x 1 m height. If the resulting density of the mixture is 850 kg m m 3 ,

determine a) the mass of each liquid inside the tank (kg m ), b) the weight of the mixture in kg f if g = 9.79

m/s 2 .

Answer 1

a)

Volume of container=πr²h

=π*0.25²*1=0.1963m³

Mass contained in cylinder=density*volume

=850*0.1963

=166.855kg

Take mass of liquid 1 to be x

Therefore mass of liquid 2=166.855-x

Volume$=\frac{mass}{density}$

Total volume =0.1963

$\frac{x}{1550}+\frac{166.855-x}{550}=0.1963$

550x + 258625.25 - 1550x =167345.75

-1000x=-91279.5

x=91.2795kg

166.855-x=166.855-91.2795=75.5755kg

Mass of liquid 1=91.2795kg

Mass of liquid 2=75.5755kg

b)

W=mg

=166.855*9.79

=1633.51N