Question

Glycerin is poured into an open U-shaped tube until the height in both sides is 20 cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 25 cm. The two liquids do not mix. What is the difference in height between the top surface of glycerin and the top surface of alcohol?

Answer 1

Answer:

0.043 m

Explanation:

From the attachment, the shaded part is the ethyl alcohol. The crossed part on the other hand, is that of glycerin.

The height of the Ethyl Alcohol is h2 = 0.25 m, it's density is ρ2 = 790 kg/m³. The density of glycerin is ρ1 = 1260 kg/m³

If we assume pressure at the two points to be the same, then

P1 = P2

ρ1.g.V1 = ρ2.g.V2

ρ1.A.h1 = ρ2.A.h2

ρ1.h1 = ρ2.h2, making h1 subject of formula

h1 = ρ2.h2 / ρ1, so that

h1 = 790 * 0.25 / 1260

h1 = 197.5 / 1260

h1 = 0.157 m

Δh = 0.2 - 0.157

Δh = 0.043 m or 4.3 cm

Answer 2

The difference in height between the top surface of glycerin and the top surface of ethyl alcohol is 0.0432 meter or 4.32 centimeter.

Given the following data:

• Height of ethyl alcohol = 25 cm to m = 0.25 m

• Hydrostatic height = 20 cm to m = 0.2 m.

Scientific data:

• Density of ethyl alcohol = 790 $kg/m^3$

• Density of glycerin = 1260 $kg/m^3$

To calculate the difference in height between the top surface of glycerin and the top surface of ethyl alcohol:

The formula for hydrostatic pressure.

Mathematically, hydrostatic pressure is given by this formula:

$P = \rho gh$

Where:

• $\rho$ is the density.

• g is the acceleration due to gravity.

• h is the height.

At constant temperature, the pressure at the top surface of glycerin in the open U-shaped tube is equal to the pressure at the top surface of ethyl alcohol:

$\rho_{g}h_{g} = \rho_{a}h_{a}$

Substituting the given parameters into the formula, we have;

$1260h_{g}=790 \times 0.25\\\\1260h_{g}=197.5\\\\h_{g} =\frac{197.5}{1260}$

Height of glycerin = 0.1568 meters.

Now, we can find the difference in height:

$Difference = 0.2 - 0.1568$

Difference = 0.0432 meter or 4.32 centimeter.

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