Post on 14-Jul-2016
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RESULTS AND CALCULATION
TEST 1 (smooth plate)
Distance from leading edge, X (m) = 0.05
Micrometer reading, y
(mm)
Static pressure (mBar)
Pitot tube pressure
manometer (mBar)
Differential manometer height, ∆ h,
(mBar)
Differential manometer height, ∆ h,
(mm)
u(m/s)
¿uU u
U (1-
uU )
0 9.4 11.4 2.0 25.60 18.08 0.81 0.150.25 9.4 11.4 2.0 25.60 18.08 0.81 0.150.50 9.6 11.6 2.0 25.60 18.08 0.81 0.150.75 9.6 11.6 2.0 25.60 18.08 0.81 0.151.00 9.6 11.8 2.2 28.16 18.97 0.85 0.131.25 9.6 12.0 2.4 30.72 19.81 0.89 0.131.50 9.6 12.4 2.6 33.28 20.62 0.92 0.071.75 9.6 12.4 2.8 35.84 21.40 0.96 0.042.00 9.6 12.4 2.8 35.84 21.40 0.96 0.042.25 9.6 12.4 2.8 35.84 21.40 0.96 0.042.50 9.6 12.6 2.8 35.84 21.40 0.96 0.042.75 9.6 12.6 3.0 38.40 22.15 0.99 0.013.00 9.6 12.6 3.0 38.40 22.15 0.99 0.013.25 9.6 12.6 3.0 38.40 22.15 0.99 0.013.50 9.6 12.6 3.0 38.40 22.15 0.99 0.013.75 9.6 12.6 3.0 38.40 22.15 0.99 0.014.00 9.6 12.6 3.0 38.40 22.15 0.99 0.014.25 9.6 12.6 3.0 38.40 22.15 0.99 0.01
Free Stream Velocity, U (m/s) = 22.37
Reynolds number, ρUx / μ = 73790.36
Graphs
Graph of y (mm) Vs uU
, (Test 1)
Graph of y (mm) Vs (uU
)(1- uU
) , (Test 1).
TEST 2 (smooth plate)
Distance from leading edge, X(m) = 0.2
Micrometer reading, y
(mm)
Static pressure (mBar)
Pitot tube pressure
manometer (mBar)
Differential manometer height, ∆ h,
(mBar)
Differential manometer height, ∆ h,
(mm)
u(m/s)
¿uU u
U (1-
uU )
0 9.4 11.4 2.0 25.60 18.08 0.78 0.170.25 9.4 11.4 2.0 25.60 18.08 0.78 0.170.50 9.4 11.8 2.4 30.72 19.81 0.86 0.120.75 9.6 12.0 2.4 30.72 19.81 0.86 0.121.00 9.6 12.2 2.6 33.28 20.62 0.89 0.11.25 9.6 12.4 2.8 35.84 21.40 0.93 0.071.50 9.6 12.4 2.8 35.84 21.40 0.93 0.071.75 9.6 12.6 3.0 38.40 22.15 0.96 0.042.00 9.6 12.8 3.2 40.96 22.88 0.99 0.012.25 9.6 12.8 3.2 40.96 22.88 0.99 0.012.50 9.6 12.8 3.2 40.96 22.88 0.99 0.012.75 9.6 12.8 3.2 40.96 22.88 0.99 0.013.00 9.6 12.8 3.2 40.96 22.88 0.99 0.013.25 9.6 12.8 3.2 40.96 22.88 0.99 0.013.50 9.6 12.8 3.2 40.96 22.88 0.99 0.01
Free Stream Velocity, U (m/s) = 23.11
Reynolds number, ρUx / μ = 15521.73 X 106.
Graphs
Graph of y (mm) Vs uU
, (Test 2)
Graph of y (mm) Vs (uU
)(1- uU
) , (Test 2).
TEST 3 (Rough plate)
Distance from leading edge, X (m) = 0.05
Micrometer reading, y
(mm)
Static pressure (mBar)
Pitot tube pressure
manometer (mBar)
Differential manometer height, ∆ h,
(mBar)
Differential manometer height, ∆ h,
(mm)
u(m/s)
¿uU u
U (1-
uU )
0 9.4 11.6 2.2 28.16 18.97 0.85 0.130.25 9.6 12.0 2.4 30.72 19.81 0.89 0.100.50 9.6 12.0 2.4 30.72 19.81 0.89 0.100.75 9.6 12.2 2.6 33.28 20.62 0.92 0.071.00 9.6 12.2 2.6 33.28 20.62 0.92 0.071.25 9.6 12.2 2.6 33.28 20.62 0.92 0.071.50 9.6 12.4 2.8 35.84 21.40 0.96 0.041.75 9.6 12.4 2.8 35.84 21.40 0.96 0.042.00 9.6 12.6 3.0 38.40 22.15 0.99 0.012.25 9.6 12.6 3.0 38.40 22.15 0.99 0.012.50 9.6 12.6 3.0 38.40 22.15 0.99 0.012.75 9.6 12.6 3.0 38.40 22.15 0.99 0.01
3.00 9.6 12.6 3.0 38.40 22.15 0.99 0.013.25 9.6 12.6 3.0 38.40 22.15 0.99 0.013.50 9.6 12.6 3.0 38.40 22.15 0.99 0.01
Free Stream Velocity, U (m/s) = 22.37
Reynolds number, ρUx / μ = 73790.36
Graphs
Graph of y (mm) Vs uU
, (Test 3)
Graph of y (mm) Vs (uU
)(1- uU
) , (Test 3).
TEST 4 (Rough Plate)
Distance from leading edge, X (m) = 0.2
Micrometer reading, y
(mm)
Static pressure (mBar)
Pitot tube pressure
manometer (mBar)
Differential manometer height, ∆ h,
(mBar)
Differential manometer height, ∆ h,
(mm)
u(m/s)
¿uU u
U (1-
uU )
0 9.4 11.2 1.8 23.04 17.16 0.74 0.20.25 9.6 11.4 1.8 23.04 17.16 0.74 0.20.50 9.6 11.4 1.8 23.04 17.16 0.74 0.20.75 9.6 11.8 2.2 28.16 18.97 0.82 0.151.00 9.6 12.0 2.4 30.72 19.81 0.86 0.151.25 9.6 12.0 2.4 30.72 19.81 0.86 0.151.50 9.6 12.2 2.6 33.28 20.62 0.89 0.11.75 9.6 12.2 2.6 33.28 20.62 0.89 0.12.00 9.6 12.4 2.8 35.84 21.40 0.93 0.072.25 9.6 12.6 3.0 38.40 22.15 0.96 0.04
2.50 9.6 12.6 3.0 38.40 22.15 0.96 0.042.75 9.6 12.8 3.2 40.96 22.88 0.99 0.013.00 9.6 12.8 3.2 40.96 22.88 0.99 0.013.25 9.6 12.8 3.2 40.96 22.88 0.99 0.013.50 9.6 12.8 3.2 40.96 22.88 0.99 0.013.75 9.6 12.8 3.2 40.96 22.88 0.99 0.014.00 9.6 12.8 3.2 40.96 22.88 0.99 0.014.25 9.6 12.8 3.2 40.96 22.88 0.99 0.01
Free Stream Velocity, U (m/s) = 23.11
Reynolds number, ρUx / μ = 15521.73 X 106.
Graphs
Graph of y (mm) Vs uU
, (Test 4)
Graph of y (mm) Vs (uU
)(1- uU
) , (Test 4).
a) Smooth plate
Test 1.
Theoretical Experimentalx = 0.05Re = 73790.36
x = 0.05Re = 73790.36
δ (mm) 0.9203 2.75δ ¿ (mm) 0.3166 0.3436θ (mm) 0.1222 0.2674
Test 2.
Theoretical Experimentalx = 0.2Re = 15521.73 X 106.
x = 0.2Re = 15521.73 X 106.
δ (mm) 0.6777 2.0δ ¿ (mm) 0.0848 0.25θ (mm) 0.066 0.1944
b) Rough plate
Test 3.
Theoretical Experimentalx = 0.05Re = 73790.36
x = 0.05Re = 73790.36
δ (mm) 0.9203 2.0δ ¿ (mm) 0.3166 0.25θ (mm) 0.1222 0.1944
Test 4.
Theoretical Experimentalx = 0.2Re = 15521.73 X 106.
x = 0.2Re = 15521.73 X 106.
δ (mm) 0.6777 2.75δ ¿ (mm) 0.0848 0.3438θ (mm) 0.066 0.2674SAMPLE CALCULATIONS:
ρoil = 784 Kg m−3
ρair = 1.204 Kg m−3
gravity, g = 9.81 m/s2
5 mbar = 64 mm
Free stream velocity, U (m/s) = Highest value of u / 0.99.
Example, Test 1:
Reynolds number = ρUx / μ
= (1.204)(22.37)(0.05) / (1.825 X 10−5)
= 73790.36.
Velocity, u = √ 2 ρoil g ∆ hρair
= √ 2 x784 x 9.81 x0.2561.204
= 18.08 m/s
Free stream velocity, U = Highest value of u / 0.99
= 22.15 / 0.99
= 22.37 m/s
u/U = 18.08 / 22.37
= 0.81
u/U (1-u/U) = 0.81 (1-0.81)
= 0.15
Calculation of Theoretical δ (boundary layer thickness), δ ¿ (displacement thickness) and θ(momentum thickness)
For smooth surface x = 0.05 m
δ = 5.0 x√ℜ
= 5.0 x 0.05√73790.36
= 0.9203
δ ¿ = 1.72 x√ℜ
= 1.72 x 0.05√73790.36
= 0.3166
θ = 0.664 x√ℜ
= 0.664 x0.05√73790.36
= 0.1222
Calculation of Experimental δ (boundary layer thickness), δ ¿ (displacement thickness) and θ(momentum thickness)
δ = 2.75 mm
δ ¿ = ∫(1− uU )dy
= ∫(1−( yδ )
17)dy
= 1/8 (δ)
= 1/8 (2.75)
= 0.3436 mm
θ=¿ ∫ uU
(1− uU
) dy
= ∫( yδ )
17 (1− y
δ
17 )dy
= 7/72 (δ)
= 7/72(2.75)
= 0.2674 mm