441
Chapter 6 x Viscous Flow in Ducts
check Re
4UQ
SPd
kg
Guessing Uoil | 900 3 ,
m
4(900)(0.071/3600)
| 16 OK, laminar
S (0.292)(0.005)
Ans.
It is not possible to find density from this data, laminar pipe flow is independent of density.
6.13 A soda straw is 20 cm long and 2 mm in diameter. It delivers cold cola,
approximated as water at 10qC, at a rate of 3 cm3s. (a) What is the head loss through the
straw? What is the axial pressure gradient wpwx if the flow is (b) vertically up or
(c) horizontal? Can the human lung deliver this much flow?
Solution: For water at 10qC, take U
Re
4 UQ
SP d
1000 kgm3 and P
1.307E3 kgm˜s. Check Re:
4(1000)(3E6 m3 /s)
1460 (OK, laminar flow)
S (1.307E3)(0.002)
Then, from Eq. (6.12), h f
128PLQ
SUgd 4
128(1.307E3)(0.2)(3E6)
| 0.204 m
S (1000)(9.81)(0.002)4
Ans. (a)
If the straw is horizontal, then the pressure gradient is simply due to the head loss:
'p
_horiz
L
Ugh f
L
1000(9.81)(0.204 m)
Pa
| 9980
0.2 m
m
Ans. (c)
If the straw is vertical, with flow up, the head loss and elevation change add together:
'p
_vertical
L
Ug(h f 'z)
L
1000(9.81)(0.204 0.2)
Pa
| 19800
0.2
m
Ans. (b)
The human lung can certainly deliver case (c) and strong lungs can develop case (b) also.