Flow through pipes, plates and channels

Question 1

u max from ū for lamina flow through pipes and plates

Answer 1

pipe: ū = 1/2 umax
plate: ū = 2/3 umax

Question 2

Poiseuille equation for laminar flow through plates

Answer 2

Δp = 12 QμL / Wh^3

Question 3

Lamina Shear stress at surface of plate and force needed to produce it

Answer 3

τ = Δp h / 2L
F = Δp W h / 2

Width (W)
Length (L)
Plate separation (h)

Question 4

Lamina Velocity of flow through parallel plates

Answer 4

u = 1/2μ Δp/L (h-y)y

Question 5

Lamina Velocity of flow through a pipe

Answer 5

u = Δp/4Lμ (R^2 - r^2)

Question 6

Lamina Volumetric flow rate through an annulus

Answer 6

Q = Δp h^3 π r / 6 μ L

Question 7

Lamina Pressure drop over length L in a pipe

Answer 7

Δp = 12μ L ū / h^2

Question 8

A good approximation for the velocity of turbulent flow

Answer 8

ū = 0.82 umax
u/umax = (r/R) ^1/n
where n is 7

Question 9

A good simplification for pipes in series that relates Q and Δp

Answer 9

Lamina flow:
Δp = RQ (Poiseuille law)
Q1 = Q2 = …
R = R1 + R2 + …

Turbulent flow:
Δp = p1 + p2 + … (Darcy equation)
Q1 = Q2 = …

Question 10

A good simplification for pipes in parallel that relates Q and Δp

Answer 10

Lamina flow:
Δp = RQ (Poiseuille law)
Δp1 = Δp2 = …
Q = Q1 + Q2 + …
1/R = 1/R1 + 1/R2 + …

Turbulent flow:
Δp1 = Δp2 = … (Darcy equation)
Q = Q1 + Q2 + …