Import Question JSON

Current Question (ID: 10460)

Question:

$\text{Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure p at points along the axis is represented by:}$

Options:

1. $\text{Graph 1: Pressure decreases in the converging section, remains low in the throat, then increases in the diverging section}$
2. $\text{Graph 2: Pressure increases in the converging section, remains high in the throat, then decreases in the diverging section}$
3. $\text{Graph 3: Pressure remains constant throughout the entire duct}$
4. $\text{Graph 4: Pressure decreases in the converging section, reaches minimum at throat, then increases in the diverging section}$

Solution:

\text{Using Bernoulli's theorem and continuity equation, as the area decreases,} \text{the velocity increases and hence, the pressure decreases.} \text{Explanation:} \text{According to Bernoulli's equation: } P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant} \text{According to continuity equation: } A_1v_1 = A_2v_2 \text{As the cross-sectional area decreases (converging section),} \text{velocity must increase to maintain mass flow rate.} \text{When velocity increases, according to Bernoulli's equation,} \text{pressure must decrease to maintain energy conservation.} \text{At the throat (minimum area), velocity is maximum,} \text{so pressure is minimum.} \text{In the diverging section, area increases, velocity decreases,} \text{and pressure increases again.} \text{This results in a pressure profile that decreases to a minimum} \text{at the throat, then increases.}

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}