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Current Question (ID: 19564)

Question:

$\text{If it takes } 5 \text{ minutes to fill a } 15 \text{ litre bucket from a water tap of diameter } \frac{2}{\sqrt{\pi}} \text{ cm, then the Reynolds number for the flow is:}$ $\text{(density of water } = 10^3 \text{ kg/m}^3 \text{ and viscosity of water } = 10^{-3} \text{ Pa.s)}$

Options:

1. $11,000$
2. $550$
3. $1100$
4. $5500$

Solution:

$\text{Hint: } R_e = \frac{\rho v d}{\eta}$ $\text{Step 1: Find the speed of fluid.}$ $\text{The volume flow rate is defined as;}$ $\Rightarrow Q = \frac{V}{t} = Av$ $\text{Rearrange above equation to get the speed;}$ $\Rightarrow v = \frac{V}{At} = \frac{4V}{\pi d^2 t} \quad \cdots (1)$ $\text{Step 2: Find the Reynolds number.}$ $\text{The Reynolds number is given by;}$ $\Rightarrow R_e = \frac{\rho v d}{\eta}$ $\text{Now, by using equation (1) replace the expression for speed (v);}$ $\Rightarrow R_e = \frac{\rho d}{\eta} \times \frac{4V}{\pi d^2 t}$ $\Rightarrow R_e = \frac{\rho}{\eta} \times \frac{4V}{\pi dt}$ $\text{Now, substitute the known values;}$ $R_e = \frac{1000}{10^{-3}} \times \frac{4 \times 15 \times 10^{-3}}{\pi \times \frac{2}{\sqrt{\pi}} \times 10^{-2} \times 5 \times 60} = \frac{10^4}{\sqrt{\pi}} = 5642$ $\text{Hence, option (4) is the correct answer.}$

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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
}