TUTORIAL TUTORIAL FST359 FST359 CHAPTER 2: CENTRIFUGE QUESTION 1 In a centrifuge operating at 70 L/minutes, 50% of the food particles required size was reduced to 15 µm (d) (d).. Given: = 1155 kg/m3 = 1053 kg/m3 = 1.5 Poise
Particle density (ps) Liquid density (pL) Liquid viscosity () i)
Calculate the feasibility value of the centrifuge. (5 marks)
ii) By using the information shown in Table 1 below, decide if this operation is feasible to be carried out in a tubular, disc, or decanter centrifuge. (1 mark) Table 1: List of centrifuge and its feasibility value Types of Centrifuge Tubular Disc Decanter Q liter/minute 10-100 2-2,000 15-2,300 -8 -8 Q/∑ m/s 5-35 x 10 8-50 x 10 500-150,000 x 10-8
ANSWER Step Step 1: Convert
into
kg ms
value
u liquid vis cos ity u 1.5Poise u 1.5
g cm s
u 0.15
1kg 1000g
100cm 1m
kg ms
Step Step 2: convert d i nto m value d 15 m
d 15 10 6 m
Step Step 3: use this fo rmul a u
gd 2 s l 18
u u
gd 2 s l 18
9.81 15 10
1155 1053
6 2
18 0.15
u 8.338 10 8
m s
Step 4: use this fo rmul a Q 2 u Q 2 u Q
Q
Q
2u
2 8.338 10 16.67 10
8
8
m s
m
s Therefore, the operation is feasible for both t ubular and disc bow l centrifu ges
QUESTION 2 In a centrifuge operating at 120 L/minutes, 50% of the food particles required size was reduced to 20 µm (d). Given: Particle density (ps) Liquid density (pL) Liquid viscosity () i)
= 1750 kg/m3 = 1250 kg/m3 = 2.5 Poise
Calculate the feasibility value of the centrifuge. (5 marks)
ii) By using the information shown in Table 1 below, decide if this operation is feasible to be carried out in a tubular, disc, or decanter centrifuge. (1 mark) Table 1: List of centrifuge and its feasibility value Types of Centrifuge Tubular Disc Decanter Q liter/minute 10-100 2-2,000 15-2,300 -8 -8 Q/∑ m/s 5-35 x 10 8-50 x 10 500-150,000 x 10-8
ANSWER Step 1: Convert = 0.25 kg/m.s
into kg/m.s value
Step 2: convert d i nto m value d = 20 x 10-6 m Step 3: use this fo rmul a u = g d 2 ( u = 43.6 x 10-8 m/s
s- l )/18µ
Step 4: use this formula Q = 2 ∑ u Q/ = 87.2 x 10 -8 m/s
Therefore, the operation is not feasible for all t ubular, decanter and disc bowl centrifuges.
QUESTION 3 In a centrifuge operating at 20 L/minutes, 50% of the food particles required size was reduced to 18 µm (d). Given: Particle density (ps) Liquid density (pL) Liquid viscosity () i)
= 1050 kg/m3 = 930 kg/m 3 = 0.5 Poise
Calculate the feasibility value of the centrifuge. (5 marks)
ii) By using the information shown in Table 1 below, decide if this operation is feasible to be carried out in a tubular, disc, or decanter centrifuge. (1 mark) Table 1: List of centrifuge and its feasibility value Types of Centrifuge Tubular Disc Decanter Q liter/minute 10-100 2-2,000 15-2,300 -8 -8 Q/∑ m/s 5-35 x 10 8-50 x 10 500-150,000 x 10-8
ANSWER Step 1: Convert = 0.05 kg/m.s
into kg/m.s value
Step 2: convert d i nto m value d = 18 x 10-6 m Step 3: use this fo rmul a u = g d 2 ( u = 42.3 x 10-8 m/s
s- l )/18µ
Step 4: use this formula Q = 2 ∑ u Q/ = 84.6 x 10 -8 m/s
Therefore, the operation is not feasible for all tubular, decanter and disc b owl centrifuges.
QUESTION 4 A 1000 L tank containing 20% salt solution (density 1130 kg/m 3 (l)) at 24oC was mixed with 17% fine sand (0.3 mm (d) diameter and density 2010 kg/m 3 (s)). If the tank was 6.5 m high (h) and the viscosity of water was 1 x 10 -3 kg/m.s (µ), estimate the time required for the sand to settle. g = 9.81 m/s 2
u = g d 2 (s-l)/18µ
t = h/u o (3 marks)
ANSWER Step 1: convert d into m value d 0.3mm d 3 10 m 4
Step 2: use this fo rmul a u u u
18
2010 1130 181 10
9.81 3 10
4 2
3
m s
Step 3: use this fo rmul a t
t
18
gd 2 s l
u 0.0043164
t
gd 2 s l
h u0 6.5m 0.0043164
m s
t 1505.8845s
h u0
QUESTION 5 A 1020 L tank containing 15% salt solution (density 1010 kg/m 3 (l)) at 14oC was mixed with 10% fine sand (0.7 mm (d) diameter and density 1910 kg/m3 (s)). If the tank was 10 m high (h) and the viscosity of water was 1 x 10 -3 kg/m.s (µ), estimate the time required for the sand to settle. g = 9.81 m/s 2
u = g d 2 (s-l)/18µ
t = h/u o (3 marks)
ANSWER Step 1: convert d into m value d = 7 x 10-4 m Step 2: use this fo rmul a u = g d 2 ( u = 0.2403 m/s
s- l )/18µ
Step 3: use this fo rmul a t = h/u o t = 41.6146 s
QUESTION 6 A 5500 L tank containing 30% salt solution (density 3700 kg/m 3 (l)) at 27oC was mixed with 12% fine sand (1.3 mm (d) diameter and density 5910 kg/m3 (s)). If the tank was 16 m high (h) and the viscosity of water was 1 x 10 -3 kg/m.s (µ), estimate the time required for the sand to settle. g = 9.81 m/s 2
u = g d 2 (s-l)/18µ
t = h/u o (3 marks)
ANSWER Step 1: convert d into m value d = 13 x 10-4 m Step 2: use this fo rmul a u = g d 2 ( u = 2.0355 m/s Step 3: use this fo rmul a t = h/u o t = 7.8604 s
s- l )/18µ
