Question

Calculate the pressure drop over a 100m length due to friction when a slurry made from 1.0-mm silica particles is pumped through a horizontal 6-cm diameter pipeline (smooth pipe) at 2.5 m/s. The slurry contains 25 per cent silica by volume. The density of silica is 2700 kg/m3, rhow = 1000 kg/m3, μw = 0.001 kg/ms. Use a value of 82 for Ω. Drag coefficient for these particles,CD, may be taken as 0.44 .

For the slurry/Pipe system in question 1, estimate the deposition velocity.

Answer 1

The answer is "2.78".

Step-by-step explanation:

Given values:

CD= 0.44

Formula:

`\bold{f_r= (v^(2))/( g(s-1)D)}`

g=9.8

s= 2.7

D= 0.06

`\to f_r=(2.5^2)/(9.8(2.7-1)0.06)\\\\`

`=(2.5 * 2.5)/(9.8 * 1.7 * 0.06 )\\\\=(6.25)/(.9996 )\\\\=6.252501`

`\phi = (82* v)/( √(cD) * f_r^(-1.5))\\\\`

`= (82 * 0.25 )/( √(0.44) * 6.25^(1.5))\\\\=2.4285\\`

`(\bigtriangleup P f_1 s_1)/(L) = (\bigtriangleup Pf_w)/(L)(1+\phi)\\`

`=(2fwSwv^2 (1+2.4285))/(D)\\\\`

`Re= (D \bar v Sw)/(M_w)\\`

`=(0.06 * 2.5 * 1000 )/(0.001)\\\\=(150 )/(0.001)\\\\= 150 * 10^(3)\\\\= 1.50 * 10^(5)\\\\`

`fw= 0.00389`

`\to (\bigtriangleup P f_1 s_1)/(L)`

`\to (2 * 0.00389 * 1000 *2.5^2 * 3.4265)/(0.06)\\\\\to 2.78`