Respuesta :
Answer:
Difference in height = 7.5 cm
Explanation:
We are given;.
Height of ethyl alcohol;h2 = 20 cm = 0.2 m
Density of glycerin: ρ1 = 1260 kg/m³
Density of ethyl alcohol; ρ2 = 790 kg/m³
To get the difference in height, the pressure at the top of the open end must be equal to the pressure at the point where the liquids do not mix since both points will be at different levels after the pouring.
Thus;
P1 = P2
Formula for pressure is; P = ρgh
Thus;
ρ1 × g × h1 = ρ2 × g × h2
g will cancel out to give;
ρ1 × h1 = ρ2× h2
Making h1 the subject, we have;
h1 = (ρ2× h2)/ρ1
h1 = (790 × 0.2)/1260
h1 = 0.125 m
Difference in height will be;
Δh = h2 - h1
Δh = 0.2 - 0.125
Δh = 0.075 m = 7.5 cm
The difference in height between the top surface of the glycerin and the top surface of the alcohol as per Pascal's law is 7.5 cm.
What is Pascal's law?
As per Pascal's law, "The pressure at any point of the vessel filled with incompressible liquid is same".
Given data -
The height of both section is, h2 = 20 cm = 0.20 m.
The density of glycerine is, [tex]\rho_{1} = 1260 \;\rm kg/m^{3}[/tex].
The density of alcohol is, [tex]\rho_{2} = 790 \;\rm kg/m^{3}[/tex].
The pressure at the top of the open end must be equal to the pressure at the point where the liquids do not mix since both points will be at different levels after the pouring. Therefore,
P1 = P2
The formula for pressure is;
P = ρgh
Thus;
ρ1 × g × h1 = ρ2 × g × h2
ρ1 × h1 = ρ2× h2
h1 = (ρ2× h2)/ρ1
h1 = (790 × 0.2)/1260
h1 = 0.125 m
Difference in height will be;
Δh = h2 - h1
Δh = 0.2 - 0.125
Δh = 0.075 m
Δh = 7.5 cm
Thus, we can conclude that the difference in height between the top surface of the glycerin and the top surface of the alcohol is 7.5 cm.
Learn more about Pascal's law here:
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