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Katen [24]
3 years ago
11

A flocculation basin equipped with revolving paddles is 60 ft long (the direction of flow). 45 ft wide, and 14 ft deep and treat

s 10 mgd. The power input to provide paddle-blade velocities of 1.0 and 1.4 fps for the inner and outer blades, respectively, is 930 ft'lb/s. Calculate the detention time, horizontal flow-through velocity, and G (the mean velocity gradient) for a water temperature of 50'F.
Engineering
1 answer:
Vinil7 [7]3 years ago
6 0

Answer:

detention time =  40.72 minutes

horizontal velocity v  = 0.295 inch/s

mean velocity gradient, G = 54.38 s^{-1}

Explanation:

given data

long = 60 ft

wide = 45 ft

deep = 14 ft

flow of water to treat = 10 mgd = 15.472 ft³/s         [1 MGD = 1.5472 ft³/s ]

inner velocities = 1.0  fps

outer velocities = 1.4  fps

power required to rotates the paddles = 930 ft-lb/s

solution

we find detention time that is

time = \frac{V}{Q}

here  Q = flow of water and  V is volume of water

so

volume of flocculation basin is = 60 × 45 × 14 = 37800 ft³

so

detention time = \frac{37800}{15.472}

detention time =  40.72 minutes

and

horizontal flow through velocity is

cross-section area of tank = 45 × 14 = 630 ft²

and we know that  Av = Q

so horizontal velocity v =  \frac{Q}{A}

horizontal velocity v =  \frac{15.472}{630}

horizontal velocity v = 0.02456 ft/s

horizontal velocity v  = 0.295 inch/s

and

now we find mean velocity gradient G at  temperature of 50'F

so formula is G = \sqrt{\frac{P}{\mu V} }      

here P is power input  and μ is  viscosity  and V is  volume of flocculation basin

so Volume of flocculation basin is 37800 ft³

and μ for 500F = 8.3197  × 10^{-6} lb-s/ft²

we take from table

so we get

G = \sqrt{\frac{930}{8.3197*10^{-6}*37800} }  

mean velocity gradient, G = 54.38 s^{-1}

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Answer:

The answers to the question are

(1) Process 1 to 2

W = 295.16 kJ/kg

Q = -73.79 kJ/kg

(2) Process 2 to 3

W = 0

Q = 1135.376 kJ/kg

(3) Process 3 to 4

W = -1049.835 kJ/kg

Q = 262.459 kJ/kg

(4) Process 4 to 3

W=0

Q = -569.09 kJ/kg

(b) The thermal efficiency = 49.9 %

(c) The mean effective pressure is 9.44 bar

Explanation:

(a) Volume compression ratio \frac{v_1}{v_2}  = 10

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Temperature T₃ = 2200 K from the isentropic chart of the Otto cycle

For a polytropic process we have

\frac{p_1}{p_2}  = (\frac{v_2}{v_1} )^n Therefore p₂ = p₁ ÷ (\frac{v_2}{v_1} )^n = (1 bar) ÷ (\frac{1}{10} )^{1.3} = 19.953 bar

Similarly for a polytropic process we have

\frac{T_1}{T_2}  = (\frac{v_2}{v_1} )^{n-1} or T₂ = T₁ ÷ (\frac{v_2}{v_1} )^{n-1} = \frac{310}{0.1^{0.3}} = 618.531 K

The molar mass of air is 28.9628 g/mol.

Therefore R = \frac{8.3145}{28.9628} = 0.287 kJ/kg⋅K

cp = 1.005 kJ/kg⋅K Therefore cv = cp - R =  1.005- 0.287 = 0.718 kJ/kg⋅K

1). For process 1 to 2 which is polytropic process we have

W = \frac{R(T_2-T_1)}{n-1} = \frac{0.287(618.531-310)}{1.3 - 1}= 295.16 kJ/kg

Q =(\frac{n-\gamma}{\gamma - 1} )W = (\frac{1.3-1.4}{1.4-1} ) 295.16 kJ/kg = -73.79 kJ/kg

W = 295.16 kJ/kg

Q = -73.79 kJ/kg

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W = 0 and Q = cv×(T₃ - T₂) = 0.718× (2200-618.531) = 1135.376 kJ/kg

W = 0

Q = 1135.376 kJ/kg

3). For process 3 to 4 which is polytropic process we have

W = \frac{R(T_4-T_3)}{n-1} = Where T₄ is given by  \frac{T_4}{T_3}  = (\frac{v_3}{v_4} )^{n-1} or T₄ = T₃ ×0.1^{0.3}

= 2200 ×0.1^{0.3}  T₄ = 1102.611 K

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W = -1049.835 kJ/kg

Q = 262.459 kJ/kg

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W = 0 and Q = cv×(T₁ - T₄) = 0.718×(310 - 1102.611) = -569.09 kJ/kg

W=0

Q = -569.09 kJ/kg

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\eta = 1-\frac{T_4-T_1}{T_3-T_2} =1-\frac{1102.611-310}{2200-618.531} = 0.499 or 49.9 % Efficient

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p_{m}  = \frac{p_1r[(r^{n-1}-1)(r_p-1)]}{ (n-1)(r-1)}  where r = compression ratio and r_p = \frac{p_3}{p_2}

However p₃ = \frac{p_2T_3}{T_2} =\frac{(19.953)(2200)}{618.531} =70.97 atm

r_p = \frac{p_3}{p_2} = \frac{70.97}{19.953}  = 3.56

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Answer:

s_max = 0.8394m

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From equilibrium of block, N = W = mg

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Since μ_k = 0.3,then F = 0.3mg

To determine the velocity of Block A just before collision, let's apply the principle of work and energy;

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m_a•v_a1 + m_b•v_b1 = m_a•v_a2 + m_b•v_b2

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3(8.744) + 2(0) = 3(v_a2) + 2(v_b2)

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