A sharp-crested weir has a crest length of 2.0 m. If the head over weir is 0.4 m, calculate the discharge using Francis formula. (Use C_d = 0.623)

The correct answer is A: 0.87 m³/s. Q = (2/3) × C_d × L × √(2g) × H^(3/2) = (2/3) × 0.623 × 2.0 × 4.43 × (0.4)^1.5 ≈ 0.87 m³/s

The overall heat transfer coefficient U in a composite system (series resistances) is determined by which method?

The correct answer is A: U = 1/(R_total) where R_total = R_conv,1 + R_cond + R_conv,2. Overall heat transfer coefficient is the reciprocal of total thermal resistance: 1/U = 1/(h₁A) + L/(kA) + 1/(h₂A). This accounts for series arrangement of convection and conduction resistances.

For a reversible reaction A ⇌ B with equilibrium constant Ke = 4, what is the maximum theoretical conversion in a batch reactor at equilibrium?

The correct answer is B: 80%. At equilibrium: Ke = [B]/[A] = 4. If initial [A]₀ = C, then at equilibrium: 4 = X/(1-X), solving X = 0.8 or 80%

In a counter-current liquid-liquid extraction process, the extraction becomes more efficient when the difference between equilibrium and operating lines increases. What does this signify?

The correct answer is B: Increased driving force for mass transfer. A larger gap between the operating line and equilibrium line indicates greater concentration difference, which increases the driving force (ΔC) for mass transfer, leading to higher transfer rates.

The Moody diagram is used to determine friction factor for pipe flow. It shows that friction factor increases with:

The correct answer is B: Increasing relative roughness and decreasing Reynolds number. In the Moody diagram, friction factor decreases with increasing Re in laminar region. In turbulent region, f increases with relative roughness (ε/D) and slightly decreases with increasing Re for rough pipes.

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Chemical Engineering

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117 Q 5 Topics Take Mock Test

Difficulty: All Easy Medium Hard 111–117 of 117

Topics in Chemical Engineering

All Mass Transfer 100 Heat Transfer 100 Fluid Mechanics 100 Chemical Reaction Engineering 100 Thermodynamics 97

Q.111 Hard Mass Transfer

For a countercurrent liquid-liquid extraction process, the Kremser equation is used. What is the minimum number of stages required if the separation factor is 2.0 and the extraction factor is 1.5?

A Less than 3 stages

B Approximately 3-4 stages

C Approximately 5-6 stages

D Cannot be determined without additional information

Correct Answer: D. Cannot be determined without additional information

EXPLANATION

The Kremser equation requires initial and final solute concentrations or minimum separation requirements, which are not provided in the question.

Test

Q.112 Hard Mass Transfer

For a binary diffusion process, the flux equation according to Fick's law in terms of mole fractions is given by:

A N_A = -cD_AB(dc_A/dz) + y_A(N_A + N_B)

B N_A = cD_AB(dy_A/dz) + y_A(N_A + N_B)

C N_A = D_AB(dρ_A/dz)

D N_A = -D_AB(d²c_A/dz²)

Correct Answer: B. N_A = cD_AB(dy_A/dz) + y_A(N_A + N_B)

EXPLANATION

The molar flux equation in terms of mole fractions is N_A = cD_AB(dy_A/dz) + y_A(N_A + N_B), accounting for bulk flow effects.

Test

Q.113 Hard Mass Transfer

Which statement about the relationship between diffusivity and molar mass is correct according to kinetic theory?

A D_AB ∝ √(T/M_total)

B D_AB is independent of molar mass

C D_AB ∝ (M_A × M_B)^(1/2)

D D_AB is inversely proportional to molecular weight

Correct Answer: A. D_AB ∝ √(T/M_total)

EXPLANATION

From Chapman-Enskog theory, D_AB ∝ T^(3/2)/(P × σ²) × √(M_total), where D_AB is inversely related to molecular mass through the collision cross-section dependency.

Test

Q.114 Hard Mass Transfer

A bioprocess company needs to calculate oxygen transfer rate in an aerated bioreactor. The volumetric mass transfer coefficient k_L·a depends on which parameters?

A Superficial gas velocity and interfacial area per unit volume only

B Liquid properties (viscosity, surface tension), aeration rate, and impeller design

C Temperature and pressure only

D Oxygen partial pressure in inlet gas

Correct Answer: B. Liquid properties (viscosity, surface tension), aeration rate, and impeller design

EXPLANATION

k_L·a in bioreactors depends on fluid mechanics (impeller speed, gas flow rate), liquid properties affecting k_L, and equipment design affecting interfacial area 'a'. Temperature indirectly affects through viscosity changes.

Test

Q.115 Hard Mass Transfer

For simultaneous heat and mass transfer in a wet bulb thermometer, the Lewis number (Le) is defined as Le = Sc/Pr. If Le = 1, what can be inferred?

A Heat and mass transfer coefficients are equal

B Thermal diffusivity equals mass diffusivity

C Both a and b are correct

D The system is at equilibrium

Correct Answer: C. Both a and b are correct

EXPLANATION

When Le = 1 (Sc/Pr = 1), both analogy relationships hold: α = D_AB and h/ρc_p = k_L, making heat and mass transfer coefficients proportionally equal.

Test

Q.116 Hard Mass Transfer

For turbulent flow in a pipe, the Colburn analogy for mass transfer is: j_D = (Sh)/(Re × Sc^(1/3)). Which correlation best estimates j_D for smooth pipes?

A j_D = 0.023 Re^(-0.2)

B j_D = 0.023 Re^(0.2)

C j_D = 0.037 Re^(-0.2)

D j_D = f/2 (where f is Fanning friction factor)

Correct Answer: A. j_D = 0.023 Re^(-0.2)

EXPLANATION

For smooth pipes in turbulent flow, j_D ≈ 0.023 Re^(-0.2), which is analogous to the Dittus-Boelert correlation for heat transfer with the Colburn j-factor approach.

Test

Q.117 Hard Mass Transfer

A pharmaceutical company is designing an absorption tower for NH₃ removal from air using H₂SO₄ solution. The Henry's law constant for NH₃ at 25°C is very small. What does this indicate about the system?

A Gas phase controls the mass transfer

B Liquid phase controls the mass transfer

C Both phases equally resist mass transfer

D Equilibrium conversion is very low

Correct Answer: A. Gas phase controls the mass transfer

EXPLANATION

A small Henry's law constant (H) for NH₃ indicates high solubility in the liquid phase. Since 1/K_L = 1/k_L + H/k_G, a small H means the gas phase resistance dominates.

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