1. [Oxygen depletion, Streeter-Phelps equation]. A company intends to discharge a treated wastewater at a volumetric flow rate of 25 % of the average river flow at a specific discharge point. The effluent is estimated to contain 25 mg/L BOD5 and 2 mg/L of dissolved oxygen. Assume there are no other discharges into the river. At a location just upstream the discharge point, the BOD5 in the river is 3 mg/L and the dissolved oxygen is 9 mg/L. The average velocity of the river water is 1.0 m/min and the average flow rate is 15 m³/min. The river has a mean depth of 1.5 m and the average river temperature is 17°C. The BOD degradation rate constant (k₁) is 0.230 d-¹ at 20°C. a) For the data given above, calculate the minimum dissolved oxygen concentration and the distance this occurs downstream from the discharge point; [Ans: DO min = 3.79 mg/L; distance @ DOmin = 7.88km] b) Draw the oxygen sag curve by calculating and plotting the oxygen deficiency for intervals of 2.5 km up to 25 km. Use a spreadsheet or graph paper to plot the computed data; c) The area surrounding the company is prone to droughts. The river flow regularly falls to an average velocity of 0.5 m/min and to a mean depth to 1 m. What effect does this have on the oxygen sag curve (plot new curve), tmax and Dmax? Assume that the river flow rate is directly proportional to the velocity and mean depth; [Ans: tmax = 4.53 days; Dmax=8.74 mg/L]
1. [Oxygen depletion, Streeter-Phelps equation]. A company intends to discharge a treated wastewater at a volumetric flow rate of 25 % of the average river flow at a specific discharge point. The effluent is estimated to contain 25 mg/L BOD5 and 2 mg/L of dissolved oxygen. Assume there are no other discharges into the river. At a location just upstream the discharge point, the BOD5 in the river is 3 mg/L and the dissolved oxygen is 9 mg/L. The average velocity of the river water is 1.0 m/min and the average flow rate is 15 m³/min. The river has a mean depth of 1.5 m and the average river temperature is 17°C. The BOD degradation rate constant (k₁) is 0.230 d-¹ at 20°C. a) For the data given above, calculate the minimum dissolved oxygen concentration and the distance this occurs downstream from the discharge point; [Ans: DO min = 3.79 mg/L; distance @ DOmin = 7.88km] b) Draw the oxygen sag curve by calculating and plotting the oxygen deficiency for intervals of 2.5 km up to 25 km. Use a spreadsheet or graph paper to plot the computed data; c) The area surrounding the company is prone to droughts. The river flow regularly falls to an average velocity of 0.5 m/min and to a mean depth to 1 m. What effect does this have on the oxygen sag curve (plot new curve), tmax and Dmax? Assume that the river flow rate is directly proportional to the velocity and mean depth; [Ans: tmax = 4.53 days; Dmax=8.74 mg/L]
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![1. [Oxygen depletion, Streeter-Phelps equation]. A company intends to discharge a treated
wastewater at a volumetric flow rate of 25 % of the average river flow at a specific discharge
point. The effluent is estimated to contain 25 mg/L BOD5 and 2 mg/L of dissolved oxygen.
Assume there are no other discharges into the river. At a location just upstream the discharge
point, the BOD5 in the river is 3 mg/L and the dissolved oxygen is 9 mg/L. The average velocity
of the river water is 1.0 m/min and the average flow rate is 15 m³/min. The river has a mean
depth of 1.5 m and the average river temperature is 17°C.
The BOD degradation rate constant (k₁) is 0.230 d-¹ at 20°C.
a) For the data given above, calculate the minimum dissolved oxygen concentration and the
distance this occurs downstream from the discharge point;
[Ans: DO min = 3.79 mg/L; distance @ DOmin = 7.88km]
b) Draw the oxygen sag curve by calculating and plotting the oxygen deficiency for intervals of
2.5 km up to 25 km. Use a spreadsheet or graph paper to plot the computed data;
c) The area surrounding the company is prone to droughts. The river flow regularly falls to an
average velocity of 0.5 m/min and to a mean depth to 1 m. What effect does this have on the
oxygen sag curve (plot new curve), tmax and Dmax? Assume that the river flow rate is directly
proportional to the velocity and mean depth;
[Ans: tmax = 4.53 days; Dmax = 8.74 mg/L]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde55ad6b-27eb-44c5-bca1-afdb32f2dfc7%2Faf1261e8-d4fa-44f0-b53a-a8816c24b427%2Fhz4qqsw_processed.png&w=3840&q=75)
Transcribed Image Text:1. [Oxygen depletion, Streeter-Phelps equation]. A company intends to discharge a treated
wastewater at a volumetric flow rate of 25 % of the average river flow at a specific discharge
point. The effluent is estimated to contain 25 mg/L BOD5 and 2 mg/L of dissolved oxygen.
Assume there are no other discharges into the river. At a location just upstream the discharge
point, the BOD5 in the river is 3 mg/L and the dissolved oxygen is 9 mg/L. The average velocity
of the river water is 1.0 m/min and the average flow rate is 15 m³/min. The river has a mean
depth of 1.5 m and the average river temperature is 17°C.
The BOD degradation rate constant (k₁) is 0.230 d-¹ at 20°C.
a) For the data given above, calculate the minimum dissolved oxygen concentration and the
distance this occurs downstream from the discharge point;
[Ans: DO min = 3.79 mg/L; distance @ DOmin = 7.88km]
b) Draw the oxygen sag curve by calculating and plotting the oxygen deficiency for intervals of
2.5 km up to 25 km. Use a spreadsheet or graph paper to plot the computed data;
c) The area surrounding the company is prone to droughts. The river flow regularly falls to an
average velocity of 0.5 m/min and to a mean depth to 1 m. What effect does this have on the
oxygen sag curve (plot new curve), tmax and Dmax? Assume that the river flow rate is directly
proportional to the velocity and mean depth;
[Ans: tmax = 4.53 days; Dmax = 8.74 mg/L]
![Required formulae
• Re-aeration:
f (mm/h) = 78200 · [U (m/s)] 0.67. [H(mm)]-0.85
fr = f20°C 0.98(20-T (°C))
●
k₂,T(h¯¹) =
Substrate degradation:
K₁,T2 = k₁,T₁ 0(T2-T₁), with T in °C, and 0=1.047 for T>20 °C and 0=1.135 for T<20 °C;
• Calculation of DO at saturation:
DO* (9)
D(t)
• Streeter-Phelps equation and derived equations
k₁ BODu,c
.
[e¯k₁t — e−k₂t] + Dc.e-k₂t
k₂-k₁
Dmax
fr(mm/h)
H (mm)
tmax
=
=
1
0.0686+0.00188432-T+0.00000612-T² '
k₁ BODu,c
k₂
1
k₂-k₁1
· In
-k₁tmax
1
(k₂-k₁) Dc
k₁ BODu,c
'
=)]
where T is in °C;](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde55ad6b-27eb-44c5-bca1-afdb32f2dfc7%2Faf1261e8-d4fa-44f0-b53a-a8816c24b427%2F5xy6w8f_processed.png&w=3840&q=75)
Transcribed Image Text:Required formulae
• Re-aeration:
f (mm/h) = 78200 · [U (m/s)] 0.67. [H(mm)]-0.85
fr = f20°C 0.98(20-T (°C))
●
k₂,T(h¯¹) =
Substrate degradation:
K₁,T2 = k₁,T₁ 0(T2-T₁), with T in °C, and 0=1.047 for T>20 °C and 0=1.135 for T<20 °C;
• Calculation of DO at saturation:
DO* (9)
D(t)
• Streeter-Phelps equation and derived equations
k₁ BODu,c
.
[e¯k₁t — e−k₂t] + Dc.e-k₂t
k₂-k₁
Dmax
fr(mm/h)
H (mm)
tmax
=
=
1
0.0686+0.00188432-T+0.00000612-T² '
k₁ BODu,c
k₂
1
k₂-k₁1
· In
-k₁tmax
1
(k₂-k₁) Dc
k₁ BODu,c
'
=)]
where T is in °C;
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