On the Velocity Distribution in Axially Symmetrical Jet

Abstract

Regarding the axially symmetrical jet, similar to the ease of plane jet. we must consider that in the expression of the shearing stress τ the second variation rate ∂²n/∂r² of the velocity component u is more predominant than the first variation rate ∂u ∂r for the points whose radial distance r is very small. If we suppose therefore that in the jet from the circular mouthed nozzle whose diameter is Dthe shearing stress τ assumes the following form.
τ=-ρl²∂u/∂r={(∂u/∂r)²+l^*2(∂²u/∂r²)²}^1/2
where both l and ^l* are proportional to the special nozzle distance x, that is,
l=l_??_, l*=l_??_,
the velocity components u and v can be represented form the standpoint of momentum transfer theory by
u=A/zΦ(λ), v=A/σx[λΦ(λ)-F^*(λ)/λ]
at the point defined by λ=σr x in the region where the central velocity U=Ax is inversely proportional to x=x^*+x₀, x^* being the nozzle distance of the observing point. The function Φ and its integrated function
F^*=∫λ0λΦ(λ)dλ
are the functions of λ solely, and can be uniquely determined only by giving the value of μ. For the practical use, it is sufficient to take
Φλ=c^-1/2λ2[1-(5/64-1/32μ)λ⁴]
As to the central velocity U, we may take after Ruden's experiment
x₀=5.18, U=6.45U₀D,
U₀ being the mouth velocity of jet.
The jet is limited at λ_s=σr_s/x=3.418, when we admit μ'=2.0. From the experimental data, we many take 1/σ=0.0687, then the jet radius r_s is given by
r_s=0.2332