Question

A pressure gauge fitted on the side of a tank filled with liquid reads 50 kPa and 100 kPa at heights of 10 m and 5 m. What is the approximate density of the liquid $\left(inkg/m^3\right)$ ? (take g = 10 $inkN/m^2)$

• A. 10
• B. 5000
• C. 1000
• D. 100

Answer 1

The correct option is C 1000



Suppose tank is filled with unknown liquid of density ${}^{\prime }\rho {}^{\prime }$ upto height of "h"

${\rho }_A=(h-10)\rho g$

${\rho }_A=50\times {10}^{3}Pagiven$

$50\times {10}^3=(h-10)\times \rho \times 10....\left(1\right)$

${\rho }_B=(h-5)\rho g$

${\rho }_B=100\times {10}^{3}Pagiven$

$100\times {10}^3=(h-5)\times \rho \times 10....\left(2\right)$

By solving two equations,

$\frac{100\times {10}^3}{50\times {10}^3}=\frac{h-5}{h-10}$

$2(h-10)=(h-5)$

$2h-20=h-5$

h = 15 m

So, put value of "h" in ( 1 )

$50\times {10}^3=(15-10)\times \rho \times 10$

$\rho =\frac{50\times {10}^3}{5\times 10}=1000kg/m^3$

$Densityofliquidintank=1000kg/m^3$