Answer to Question #295912 in Molecular Physics | Thermodynamics for Manuel

Question

The pressure below the depth of 25 m of a homogenous fluid is 50.473 psi.

Calculate specific weight in kN/m3,density of fluid in kgm/m3 and its specific

gravity.

Answer 1

The specific weight can be found using the relationship with the density of the fluid, the acceleration of gravity and the depth where the pressure was measured:

$P=\rho g h=\gamma h \\ \implies \gamma = \dfrac{P}{h}=\frac{50.473\,\cancel{psi}}{25\,m}\Big(\frac{101.325 \frac{kN}{m^2}}{14.696\,\cancel{psi}}\Big) \\ \gamma =13.920 \frac{kN}{m^3}=13920 \frac{kg}{m^2s^2} \\ \text{The density of the fluid will be: } \\ \rho =\frac{\gamma}{g}=\frac{13920 \frac{kg}{m^2s^2} }{ 9.807\frac{m}{s^2} }= 1419.4 \frac{kg}{m^3} \\ \text{The specific gravity can be calculated as:} \\ SG=\frac{\rho}{\rho_{H_2O}}=\frac{1419.4 \frac{kg}{m^3}}{1000 \frac{kg}{m^3}}=1.4194$

In conclusion, the specific weight of the fluid is 13.920 kN/m³, the density is 1419.4 kg/m³, and the specific gravity is 1.4194.