sm7 001

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PROBLEM 7.1 
 
KNOWN: Temperature and velocity of fluids in parallel flow over a flat plate. 
 
FIND: (a) Velocity and thermal boundary layer thicknesses at a prescribed distance from the leading 
edge, and (b) For each fluid plot the boundary layer thicknesses as a function of distance. 
 
SCHEMATIC: 
 
 
ASSUMPTIONS: (1) Transition Reynolds number is 5 × 105. 
 
PROPERTIES: Table A.4, Air (300 K, 1 atm): ν = 15.89 × 10-6 m2/s, Pr = 0.707; Table A.6, Water (300 
K): ν = μ/ρ = 855 × 10-6 N⋅s/m2/997 kg/m3 = 0.858 × 10-6 m2/s, Pr = 5.83; Table A.5, Engine Oil (300 K): 
ν = 550 × 10-6 m2/s, Pr = 6400; Table A.5, Mercury (300 K): ν = 0.113 × 10-6 m2/s, Pr = 0.0248. 
 
ANALYSIS: (a) If the flow is laminar, the following expressions may be used to compute δ and δt, 
respectively, 
 
 t1/ 2 1/ 3
x
5x
Re Pr
δδ δ= = 
where 
( ) 2
x
1m s 0.04 mu x 0.04 m s
Re ν ν ν
∞= = = 
 
Fluid Rex δ (mm) δt (mm) <
Air 2517 3.99 4.48 
Water 4.66 × 104 0.93 0.52 
Oil 72.7 23.5 1.27 
Mercury 3.54 × 105 0.34 1.17 
 
(b) Using IHT with the foregoing equations, the boundary layer thicknesses are plotted as a function of 
distance from the leading edge, x. 
0 10 20 30 40
Distance from leading edge, x (mm)
0
2
4
6
8
10
B
L 
th
ic
kn
es
s,
 d
el
ta
 (m
m
)
Air
Water
Oil
Mercury 
0 10 20 30 40
Distance from leading edge, x (mm)
0
1
2
3
4
5
B
L 
th
ic
kn
es
s,
 d
el
ta
t (
m
m
)
Air
Water
Oil
Mercury 
 
COMMENTS: (1) Note that δ ≈ δt for air, δ > δt for water, δ >> δt for oil, and δ < δt for mercury. As 
expected, the boundary layer thicknesses increase with increasing distance from the leading edge. 
 
(2) The value of δt for mercury should be viewed as a rough approximation since the expression for δ/δt 
was derived subject to the approximation that Pr > 0.6.