A liquid mixture containing 40.0 wt% n-octane and the balance n-decane flows into a tank mounted on a balance. The mass in kg indicated by the scale is plotted against time. The data fall on a straight line that passes through the points (t = 3 min, m = 150 kg) and (t= 10 min, m = 250 kg).
(a) Estimate the volumetric flow rate of the liquid mixture.
(b) What does the empty tank weigh?
.
(a)
Interpretation:
Volumetric flow rate of the mixture is to be calculated.
Concept introduction:
Volumetric flow rate of a fluid is the volume of a fluid that passes per unit time. It is mathematically represented as follows:
Volumetric flow rate =
Here,
Answer to Problem 5.1P
19.85 m3/min
Explanation of Solution
Given Information: Density of n-Octane =
Average density of the mixture = avg
Given graph is a straight line with slope as follows:
=
Putting the values, =
=19.85 m3/min
(b)
Interpretation:
Weight of empty tank is to be calculated.
Concept introduction:
A straight line equation is y = mx + c, where,
y = y-axis coordinate
x = x- axis coordinate
m = slope of line
c = intercept of straight line
Weight of a substance = Mass of substance
Answer to Problem 5.1P
1050.16 N
Explanation of Solution
The equation is a straight line with equation
m = at + c
where,
m = mass
a = slope of line
t = time
c = intercept
Mass of empty tank is mass at t = 0
i.e.
m = 0 + c
Mass of empty tank = intercept of the straight line
a =
a = 14.28 kg/min
At t = 3 min, m =150 kg
So,
150 = (14.28) (3) + c
c = 107.16
Therefore, mass of empty tank = 107.16 kg
Now, weight can be calculated using the following formula:
Here, g is acceleration due to gravity.
Putting the values,
W = 107.16
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