Question

A rectangular open channel (concrete n=0.012) has a slope of 0.12 ft/ft, and a cross sectional area of 120 square feet. The water is 50 deg F, with a density of 1.94 slugs/ft3, and a dynamic viscosity of 2.73 x 10-5 lbf-s/ft2. If the water surface has 1.0 foot of free board at peak flow of 870.0 cubic feet per second, is the flow laminar or turbulent? (prove with calculations).

Answer 1

Ans) Given,

Manning roughness coefficient(N) = 0.012

Slope(S) = 0.12 ft/ft

Cross sectional area(A) = 120 sqft

Density of water() = 1.94 slugs/ft³ or 62.4 lb/ft³

Peak flow(Q) = 870 cu.ft/sec

We know,

Q = (1.49A/N) R^2/3 S^1/2

where, R = Hydraulic mean depth

Putting values,

870 = (1.49x120/0.012) R^2/3 (0.12)^0.5

870 = 5161.51 R^2/3

R = 0.07 ft

To determine whether the flow is Laminar or Turbulent we have to calculate Reynold number (Re),

Re = RV/

where, V = velocity of fluid

= dynamic viscosity of fluid (2.73 x 10^-5 lbf-s/ft²)

V = Q/A

= 870/120

= 7.25 ft/s

Re = 62.4 x 7.25 x 0.07 / (2.73 x 10^-5)

Re = 1160000 > 2000

Since Reynold number of flow is greater then 2000, flow is turbulent