Glycerin, of density 1260.0 kg/m3, is poured into an open U-shaped tube. Ethyl alcohol, of density 790.0 kg/m3, is then poured into one arm until the height of the alcohol column is 21.4 cm. The two liquids do not mix. What is the difference in height between the top surface of the glycerin and the top surface of the alcohol?
The height of the columns must weigh the same to be in equilibrium.
What is the weight of 21.4cm of ethanol?
weight= height*area*density*g
set that equal to the weight of the glycerol, and you have the height of the glycerol.
how do you find the area?
notice area is on both sides of the equation, it will divide out if the area of the tube is constant.
1260 kg/m^3 x 9.8m/s^2 x 0.241m = 790kg/m^3 x 9.8m/s^2 x h
h = 0.384m
difference = 0.384 - 0.214 = 0.170 m
this answer was incorrect. what am i doing wrong?
hmmmm.
Ok, then the rationale is wrong. Some of the glycerol is on the alcohol side.
weight of glycerol side= weight of ethanol side, but some of the glycerol is on the alcohol side to do that.
thinking. give me a few minutes.
Let me see if I can get some other thinking here....again, a few minutes.
Ok, I am officially stuck. My mind is not working. I will try to return again on this.
okay...no problem
it worked for me. but, i had to subtract the answer i got for the height from the provided height.
To find the height difference between the top surface of the glycerin and the top surface of the alcohol, we need to understand the principle of hydrostatic pressure.
In this case, the open U-shaped tube contains two different liquids - glycerin and ethyl alcohol. Since the two liquids do not mix, they will settle at different heights in the U-shaped tube.
The hydrostatic pressure at any given point in a fluid is given by the formula:
P = ρgh
Where:
P = pressure
ρ = density of the liquid
g = acceleration due to gravity
h = height of the liquid column
Now, let's calculate the height difference:
For glycerin:
Density (ρ1) = 1260.0 kg/m³
Height (h1) = ? (unknown)
For ethyl alcohol:
Density (ρ2) = 790.0 kg/m³
Height (h2) = 21.4 cm = 0.214 m (given)
Since the pressure at the top surface of the glycerin and the alcohol are equal (since they are in contact with the atmosphere), we can write:
P1 = P2
ρ1gh1 = ρ2gh2
Now we can rearrange the equation to solve for h1:
h1 = (ρ2gh2) / (ρ1g)
Plugging in the given values:
h1 = (790.0 kg/m³ * 9.8 m/s² * 0.214 m) / (1260.0 kg/m³ * 9.8 m/s²)
Calculating the values:
h1 = 0.115 m
Therefore, the height difference between the top surface of the glycerin and the top surface of the alcohol is 0.115 meters.