Question

example 2
water and oil are placed in the two arms of a glass u - tube as shown. if they
come to rest as indicated, what is the density of the oil?
solution:
we know that, ( p_a = p_d )
and
( p_a = p_a+
ho_wgh_w )
( p_d = p_a+
ho_{oil}gh_o )
then (
ho_wgh_w=
ho_{oil}gh_o ) and
(
ho_{oil}=
ho_w\frac{h_w}{h_o} )
substitute the following values, ( h_w = 135mm ) and ( h_o = 147.3mm )

Explanation:

Step1: Substitute values into formula

Given \(
ho_{oil}=
ho_{w}\frac{h_{w}}{h_{o}} \), \(
ho_{w} = 1000\ kg/m^{3}\), \(h_{w}=135\ mm\), \(h_{o}=147.3\ mm\)

$$ ho_{oil}=1000\times\frac{135}{147.3} $$

Step2: Calculate the value

$$ ho_{oil}=\frac{135000}{147.3}\approx916.5\ kg/m^{3} $$

Answer:

The density of the oil is approximately \(916.5\ kg/m^{3}\)