Finding Density Constant for Part (c) of Question

In summary, the conversation is about finding the density of a soft drink in order to answer part (c) of a question involving a bottling plant. The person is seeking help as they are stumped and suggests using the density of water as a possible assumption.
  • #1
WY
28
0
Hey I am completely stumped as to how to find the density in this following question so I can answer part (c)
Q: At a bottling plant soft drink flows in a pipe at a rate that would fill 200 375mL cans per minute. At point 1 in the pupe the gauge pressure is 152 kPa and the crossectional area is 8cm^2. At point 2, 1.35 m above point 1, the cross sectional area is 2cm^2. Find
(a) the volume flow rate - which I have found
(b) the flow speeds at points 1 and 2 - which I also have found
(c) the gauge pressure at point 2 -this one has got me in a spin :smile:

Can someone help me out?
Thanks in advance!
 
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  • #2
WY said:
Hey I am completely stumped as to how to find the density in this following question so I can answer part (c)
If they didn't give you the density of the soft drink, you'll have to make some assumptions. I'd take the density to be that of water. (Of course, that's not quite right. Sugar-laden sodas probably have a density greater than water; diet sodas, less.)
 
  • #3


To find the density in this question, we can use the continuity equation, which states that the volume flow rate at one point in a pipe is equal to the volume flow rate at another point in the pipe. In other words, the amount of fluid entering a pipe must be equal to the amount of fluid leaving the pipe.

Since we already have the volume flow rate and flow speeds at points 1 and 2, we can use the continuity equation to find the density. The equation is:

ρ = m/V = ρ1A1v1/ A2v2

Where:
ρ = density
m = mass
V = volume
A1 = cross sectional area at point 1
v1 = flow speed at point 1
A2 = cross sectional area at point 2
v2 = flow speed at point 2

Plugging in the values from the question, we get:

ρ = ρ1(8cm^2)(v1)/(2cm^2)(v2)

Since we don't have the density at point 1, we can use the ideal gas law to find it. The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. Since we are dealing with a liquid, we can assume that n and R are constant and cancel out. Therefore, we can rearrange the equation to solve for density:

ρ = P/RT

Plugging in the values for pressure, temperature, and the gas constant, we get:

ρ1 = (152 kPa)/(8.31 J/molK)(298 K) = 0.059 kg/m^3

Now, we can plug this value into our original equation to solve for the density at point 2:

ρ = (0.059 kg/m^3)(8cm^2)(0.5 m/s)/(2cm^2)(1.5 m/s) = 0.01475 kg/m^3

Therefore, the density at point 2 is approximately 0.01475 kg/m^3. This can then be used to find the gauge pressure at point 2 using the ideal gas law:

P2 = ρ2RT = (0.01475 kg/m^3)(8.31 J/molK)(298 K) = 36.9 kPa

 

FAQ: Finding Density Constant for Part (c) of Question

What is the purpose of finding the density constant for part (c) of the question?

The purpose of finding the density constant is to determine the relationship between the mass and volume of a substance. This constant can be used to calculate the density of any given sample of the substance.

How do you calculate the density constant for part (c) of the question?

The density constant can be calculated by dividing the mass of the substance by its volume. This will give you the density of the substance, which can then be used as a constant for future calculations.

What units are used for the density constant?

The units used for the density constant will depend on the units used for the mass and volume of the substance. For example, if the mass is measured in grams and the volume in cubic centimeters, then the density constant will have units of grams per cubic centimeter (g/cm3).

Is the density constant the same for all substances?

No, the density constant will vary depending on the substance. Each substance has its own unique density, which is determined by its chemical composition and physical properties.

How is the density constant used in scientific research?

The density constant is an important factor in many scientific studies, especially in fields such as chemistry and materials science. It can be used to identify unknown substances, measure the purity of a substance, and predict the behavior of a substance in different conditions.

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