Name :_________________ Quiz: No. 11 Time: 15 minutes Student ID# : ____________ Course: ME 5160, Fall 2021
--- The exam is closed book and closed notes.
Air at 20°C and 1 atm (ρ=1.2 kg/m
3; µ=1.8E-5 kg/m.s.) flows at 3 m/s past a sharp flat plate 2 m wide and 1 m long. (a) Determine if the flow is laminar or turbulent at the end of the plate? (b) What is the wall shear stress at the end of the plate? (c) What is the air velocity at a point 4.5 mm normal to the end of the plate? (d) What is the total friction drag on the plate, considering both sides of the plate?
Equations:
Laminar Boundary Layer: 𝑐
𝑓=
2𝜏𝑤𝜌𝑈2
=
0.664𝑅𝑒𝑥1/2
; 𝐶
𝐷=
1 𝐷2𝜌𝐴𝑈2
=
1.328𝑅𝑒𝐿1/2
; velocity profile given in the Table below:
Turbulent Boundary Layer: 𝑐
𝑓=
2𝜏𝑤𝜌𝑈2
≈
0.027𝑅𝑒𝑥1/7
; 𝐶
𝐷=
1 𝐷2𝜌𝐴𝑈2
=
0.031𝑅𝑒𝐿1/7
; velocity profile:
𝑢𝑈
≈ (
𝑦𝛿
)
1 7
where
𝛿𝑥
≈
0.16𝑅𝑒𝑥1/7
Name :_________________ Quiz: No. 11 Time: 15 minutes Student ID# : ____________ Course: ME 5160, Fall 2021
---
Solution:
KNOWN: U, L, b
FIND: Re
L; τ
w(L); u(y=4.5mm); D
ASSUMPTIONS: boundary layer flow with zero pressure gradient ANALYSIS:
(a)
(b)
(c)
(d)
(2)
(1)
(0.5) (0.5)
(0.5)
(0.5) (0.5) (0.5)
(0.5) (0.5)
(0.5) (0.5)
(0.5)
(0.5)
(0.5) (0.5)
