固体粒子の水力輸送に関する研究 (第1報)

傾斜管における圧力損失について

抄録

For the hydraulic transportation of solid material the authors tried to develop the pressure drop in inclined pipe and as the results of theoretical and experimental studies the following conclusions were obtained.
(1) The increase of pressure drop Δp_s due to the solid material was expressed as follows,
ΔP_s=λ_s ΔL/D γwυ²m/2g
Where the coefficient λ_s was expressed in the case of constant velocity and concentration of mixtures
λ_s=η₀Ψ=η₀· (d_s/D)^-1(1-ζ)²/ζ
ζ=υ_{s/υm=1-1/Fγ √ 4(ρ -1) /3CD0(ds/D) (μscosθ +ρsinθ ρ-1)}
(2) The hydraulic gradient i along the pipe was expressed as follows,
i=i_w (1+φ·k)
where the coefficient of pressure drop φ was expressed as follows by the exprience using the sand (ρ=2.75, d_s=0.4mm)
φ=φ₀F_γ^-n=(100-23.6θ) F_γ-(^{4.4-2.1θ0.342})
Nonmenclature
d_s, D=equivalent diameter of solid and inner diameter of pipe (m)
υ_s, υ_m=mean velocity of solid and mixtures (m/s)
i_w=hydraulic gradient with water alone (mAq/m)
F_r=Froud's Number=v_m/g.D
ρ=specific gravity of solid
θ= inclination of pipe (rad.)
μ_s, C_D0=frictional coefficient for pipe and drag coefficient of solid
k=rate of mixture
η₀, φ₀, n=constants