If there are two pipes of 8 mm and 10mm diameter,former carrying Helium and later carrying Nitrogen. Which pipe will have higher mass flow rate and which will have higher volume flow rate? Why

Question

Accepted Answer

The pipe with 10mm diameter carrying Nitrogen will have higher mass flow rate due to higher density. The pipe with 8mm diameter carrying Helium will have higher volume flow rate due to lower density.

Nitrogen has a higher density than Helium, so the pipe with 10mm diameter will have higher mass flow rate
Helium has a lower density than Nitrogen, so the pipe with 8mm diameter will have higher volume flow rate

Accepted Answer

Mass Flow Rate:
Mass flow rate is given by the formula:

𝑚
˙
=
𝜌
⋅
𝐴
⋅
𝑣
m
˙
 =ρ⋅A⋅v

where:

𝑚
˙
m
˙
  is the mass flow rate,
𝜌
ρ is the density of the fluid,
𝐴
A is the cross-sectional area of the pipe,
𝑣
v is the velocity of the fluid.
Helium (8 mm diameter pipe):

Helium has a much lower density (
𝜌
𝐻
𝑒
ρ 
He
​
 ) compared to Nitrogen.
Given the same velocity 
𝑣
v in both pipes, the mass flow rate 
𝑚
˙
𝐻
𝑒
m
˙
  
He
​
  for Helium will be lower because of its lower density.
Nitrogen (10 mm diameter pipe):

Nitrogen has a higher density (
𝜌
𝑁
2
ρ 
N 
2
​
 
​
 ) compared to Helium.
At the same velocity 
𝑣
v as Helium, the mass flow rate 
𝑚
˙
𝑁
2
m
˙
  
N 
2
​
 
​
  for Nitrogen will be higher due to its higher density.
Conclusion for Mass Flow Rate: The pipe carrying Nitrogen (10 mm diameter) will have a higher mass flow rate (
𝑚
˙
𝑁
2
>
𝑚
˙
𝐻
𝑒
m
˙
  
N 
2
​
 
​
 > 
m
˙
  
He
​
 ) because Nitrogen has a higher density than Helium.

Volume Flow Rate:
Volume flow rate is calculated using the formula:

𝑄
=
𝐴
⋅
𝑣
Q=A⋅v

where:

𝑄
Q is the volume flow rate,
𝐴
A is the cross-sectional area of the pipe,
𝑣
v is the velocity of the fluid.
Helium (8 mm diameter pipe):

Despite Helium having a lower mass flow rate, its volume flow rate 
𝑄
𝐻
𝑒
Q 
He
​
  can potentially be higher than that of Nitrogen if the velocity 
𝑣
v of Helium is higher than that of Nitrogen, given the smaller cross-sectional area.
Nitrogen (10 mm diameter pipe):

Nitrogen, with its larger diameter, will have a larger cross-sectional area 
𝐴
A.
To match or exceed the volume flow rate of Helium, Nitrogen would need a higher velocity 
𝑣
v.
Conclusion for Volume Flow Rate:

If the velocities 
𝑣
𝐻
𝑒
v 
He
​
  and 
𝑣
𝑁
2
v 
N 
2
​
 
​
  are equal, the volume flow rate 
𝑄
𝐻
𝑒
Q 
He
​
  will be higher in the pipe carrying Helium (8 mm diameter) because of its smaller cross-sectional area 
𝐴
𝐻
𝑒
A 
He
​
 .
If the velocities 
𝑣
𝐻
𝑒
v 
He
​
  and 
𝑣
𝑁
2
v 
N 
2
​
 
​
  are different and 
𝑣
𝑁
2
>
𝑣
𝐻
𝑒
v 
N 
2
​
 
​
 >v 
He
​
 , then the pipe carrying Nitrogen (10 mm diameter) could potentially have a higher volume flow rate 
𝑄
𝑁
2
Q 
N 
2
​
 
​
 .
Summary:

Mass Flow Rate: Nitrogen (10 mm diameter) will have a higher mass flow rate due to its higher density compared to Helium.
Volume Flow Rate: Helium (8 mm diameter) will have a higher volume flow rate if the velocities are such that 
𝑣
𝐻
𝑒
>
𝑣
𝑁
2
v 
He
​
 >v 
N 
2
​
 
​
 , because of its smaller cross-sectional area.

Accepted Answer

10 mm diameter pipe carrying nitrogen will have both a higher mass flow rate and a higher volume flow rate compared to the 8 mm diameter pipe carrying helium. This is primarily due to the larger cross-sectional area of the pipe, which allows for greater fluid flow. Additionally, the higher density of nitrogen compared to helium contributes to the higher mass flow rate.

If there are two pipes of 8 mm and 10mm diameter,former carrying Helium and later carrying Nitrogen. Which pipe will have higher mass flow rate and which will have higher volume flow rate? Why

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