Answer:
a) -8 lb / ft^3
b) -70.4 lb / ft^3
c) 54.4 lb / ft^3
Explanation:
Given:
- Diameter of pipe D = 12 in
- Shear stress t = 2.0 lb/ft^2
- y = 62.4 lb / ft^3
Find pressure gradient dP / dx when:
a) x is in horizontal flow direction
b) Vertical flow up
c) vertical flow down
Solution:
- dP / dx as function of shear stress and radial distance r:
(dP - y*L*sin(Q))/ L = 2*t / r
dP / L - y*sin(Q) = 2*t / r
Where dP / L = - dP/dx,
dP / dx = -2*t / r - y*sin(Q)
Where r = D /2 ,
dP / dx = -4*t / D - y*sin(Q)
a) Horizontal Pipe Q = 0
Hence, dP / dx = -4*2 / 1 - 62.4*sin(0)
dP / dx = -8 + 0
dP/dx = -8 lb / ft^3
b) Vertical pipe flow up Q = pi/2
Hence, dP / dx = -4*2 / 1 - 62.4*sin(pi/2)
dP / dx = 8 - 62.4
dP/dx = -70.4 lb / ft^3
c) Vertical flow down Q = -pi/2
Hence, dP / dx = -4*2 / 1 - 62.4*sin(-pi/2)
dP / dx = -8 + 62.4
dP/dx = 54.4 lb / ft^3
Answer:
The minimum required flow rate of fresh air that needs to be supplied to the lounge is 390L/s.
The diameter of the duct mus be of 24.9cm at least if thte air velocity is not to exceed 8m/s.
Explanation:
First, in order to find the minimum required flow rate of fresh air, we need to take the ASHRAE standard and multiply it by the number of heavy smokers, so we get:

This value can be converted to 

Once we got this value we use the volumetric flow formula, which tells us that:

where A is the area of the duct and v is the velocity of the air flow.
We also know that:

so we can substitute that into our equation, so we get:

which can be solved for the diameter, which yields:

and we can next substitute the values the problem provides us with:

so the duct must have a diameter of at least 24.9cm for the velocity not to exceed 8m/s.
Answer:
The distance from the entrance at which the flow becomes fully developed (entrance lenght) is:

Explanation:
First, we need to know if the flow is laminar or turbulent using the equation for the Reynolds number in a circular tube, which is:
(Equation 1)
We know that for
, the flow is laminar
, the flow is turbulent
Then, tanking into account that for air at 20 kPa and 5°C, kinematic viscosity
is
(taken from Table A-9, Cengel's book), we use the equation 1 ,

And, we can conclude that the flow is laminar. Then, we can use the relationship between the entrance length
, which is the distance from the entrance at wich the flow becomes fully developed, and diameter for a laminar flow in a circular tube, which is:

And we obtain,

Answer:
The outer surface temperature is 196.2 C which is lower than 200 C thus TBC layer of 0.028 m thickness will be sufficient to prevent fire hazard.