Let's solve each part step by step: --- ## (a) Organic nitrogen (org-N) flux density **Given:** - Org-N concentration, \( C = 10 \) mg/L - Water seeps into soil at rate, \( v = 2 \) cm/hr ### **Step 1: Convert units as necessary** - \( C = 10 \) mg/L = \( 0.01 \) g/L = \( 0.01 \) g/1000 cm³ = \( 1 \times 10^{-5} \) g/cm³ ### **Step 2: Flux density formula (advection)** The advective flux density \( J \) is given by: \[ J = v \cdot C \] where: - \( v \) is the velocity (cm/hr) - \( C \) is the concentration (g/cm³) ### **Step 3: Plug in the values** \[ J = 2 \ \text{cm/hr} \times 1 \times 10^{-5} \ \text{g/cm}^3 = 2 \times 10^{-5} \ \text{g/(cm}^2\text{·hr)} \] --- ### **Final Answer (a):** \[ \boxed{2 \times 10^{-5} \ \text{g/(cm}^2\text{·hr)}} \] --- ## (b) Salt flux in a horizontal tube (diffusive flux) **Given:** - Tube length, \( L = 10 \) cm - Seawater concentration, \( C_1 = 30 \) g/L - Freshwater concentration, \( C_2 = 0 \) g/L - Diffusion coefficient, \( D = 10^{-5} \) cm²/s ### **Step 1: Convert concentrations** - \( C_1 = 30 \) g/L = \( 0.03 \) g/cm³ - \( C_2 = 0 \) g/cm³ ### **Step 2: Fick's First Law (diffusive flux)** \[ J = -D \frac{dC}{dx} \] For a steady state, linear concentration gradient: \[ \frac{dC}{dx} = \frac{C_2 - C_1}{L} = \frac{0 - 0.03}{10} = -0.003 \ \text{g/cm}^4 \] ### **Step 3: Plug in the values** \[ J = - (10^{-5} \ \text{cm}^2/\text{s}) \times (-0.003 \ \text{g/cm}^4) \] \[ J = 3 \times 10^{-8} \ \text{g/(cm}^2\text{·s)} \] --- ### **Final Answer (b):** \[ \boxed{3 \times 10^{-8} \ \text{g/(cm}^2\text{·s)}} \] --- ## (c) CO₂ flux in exhaust pipe (advective flux) **Given:** - Gas velocity, \( v = 30 \) cm/s - CO₂ concentration, \( C = 0.05 \) g/L ### **Step 1: Convert concentration** - \( C = 0.05 \) g/L = \( 0.00005 \) g/cm³ ### **Step 2: Advective flux formula** \[ J = v \cdot C \] ### **Step 3: Plug in the values** \[ J = 30 \ \text{cm/s} \times 0.00005 \ \text{g/cm}^3 = 0.0015 \ \text{g/(cm}^2\text{·s)} \] --- ### **Final Answer (c):** \[ \boxed{0.0015 \ \text{g/(cm}^2\text{·s)}} \] --- ## **Summary Table** | Part | Flux Density | |------|--------------| | (a) | \(2 \times 10^{-5}\) g/(cm²·hr) | | (b) | \(3 \times 10^{-8}\) g/(cm²·s) | | (c) | \(0.0015\) g/(cm²·s) |

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