Chemical Technology April 2016

PUMPS & VALVES

less than 0,5 mm in size, and we are rather doing more of a dredging operation where the gravel at the suction inlet is much larger and could be termed a ‘heterogeneous slurry’. In this case, it is probably more practical to choose the size of suction and discharge lines, assume their lengths from the probable location on the stream bank, and using the principal of a minimum velocity V L in the suction line to maintain the gravel in suspension, use these numbers to determine the production rate of gravel and the pump duty. We can then vary the suction line size to obtain the optimum velocity. There are a number of historical formulae, deduced mainly from empirical testing, that allow us to determine the minimum velocity, V L , required in the suction hose to prevent settling. Depending on the assumed average gravel size (d 50 ) the formulae used could vary from the pumping of a slurry where the average size is small, right up to a fairly large gravel size which then almost constitutes a dredging operation. An initial assumption of a 6” (15,41 cm) diameter suction hose produced an excess of material to sort; thus the suc- tion hose has been reduced to 2” (5,25 cm) diameter. For the purposes of example, assume we install a 2” diameter plastic suction hose of about 50 m in length. Then assume we are pumping a gravel/water mixture of about a C V or volume concentration of 15 %, the gravel and mud average size of about 3 mm, or d 50 = 3 mm.

The suction hose will be in the stream and the discharge will be from the pump to the ‘trommel’. The illustration above describes the system. What would be the pump type, materials of construction, speed, required power, Net Positive Suction head require- ments, etc? As many of the variables in the pumping system will probably be confirmed on the site, v-belts from the motor to the pump will be installed to allow changes in the pump speed to ensure optimum operation. We will refer to the ‘mixture’ of gravel, sand and mud as a ‘slurry’ for the purposes of the calculation. Depending on the coarseness of the gravel, the slurry can be categorised and, for example, a Category ‘C’ slurry is the suction dredging of gravel and coarse sand [5]. Cw is usually less than 20 % as it is difficult to manually ensure a higher concentration by dragging the suction hose through the silt. Assume the Cw (or Concentration of solids in the slurry, by mass %) = 20 % = x t/hr Mass of water will be 80 % of slurry or x/20 % x 80 % = 4 x t/hr Mass of water + mass of gravel = (4 x + x) = 5 x t/hr SG of gravel is 2,65 So slurry mass will have a mass of water equivalent to x/2,65 t/hr Total mass of water would be 4 x + x /2,65 = 4,38 x t/hr The SG of slurry mix would be = 5 x /4,38 x =1,14 The water has a density of 1 000 kg/m 3 , slurry 1 140 kg/m 3 , 1 000 kg/tonne Slurry flow of 17,1 m 3 /hr converted to tonnes/hr = 17,1 x1 140/1 000 = 19,494 t/hr 5 x = 19,494 hence x = 3,9 t/hr of gravel. Assuming 50 kg sorting bags, production would be about 450 bags per 6-hour day. Friction head Hf for the pipeline to select the pump and power The friction losses in the lines can be calculated by a num- ber of means, the most common being to determine the equivalent lengths of pipe for the hoses and fittings and so obtain the friction loss. The Reynold’s number for the system can be calculated Re and using the Moody ‘Friction factors for pipe flow’, graph, we can obtain the fanning friction factor f . Using Darcy’s formula for friction head loss h L h L = (f L /D + K ent + K exit ) V 2 /2g The Dynamic head loss is now calculated as the friction

Assume the SG of the wet gravel With an average particle size of

S=2,65

d

=3 mm

50

Concentration of solids Discharge head, static

Cw=20 % by mass

Zb=2 m

Suction head

Za= -5 m (negative) Suction hose 50 m of 0,0525 m dia, Discharge hose 3 m Foot strainer on the suction hose

Length of hoses

Number of valves and fittings

From Durand’s settling velocity equation V L [2]: V L = F L √(2gD(S-1)) where V L = minimum velocity in the line to maintain gravel flow F L = is the Modified Froude number =1,34 an empirical coefficient [3] for this slurry size 2g = g being gravitational acceleration or 9,81 m/sec 2 D = diameter of pipe in metres for 2” line = 0,0525 m S = solids specific gravity = 2,65 V L =1,4√(2 x 9,81 x 0,0525 x (2,65-1)) =1,825 say 1,8m/sec With a safety factor of about 20 % we will use 1,8 x 1,2 = 2,2 m/sec as the velocity in the line. There are a number of other correlations available to determine the critical velocity, or V C, which is similar to the V L or minimum velocity, to maintain gravel suspension. For example, the K C Wilson [4] equations; however, the Durand values are more conservative and so are used here as an example.

V= 4Q/πD 2 so Q in m 3 /sec = 3,142 x 0,00275 x 2,2/4 = 0,00475 m 3 /sec or 17,1 m 3 /hr (2” dia = 0,0525 m)

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Chemical Technology • April 2016