Calculate the speed of efflux of kerosene oil from an orifice of a tank in which pressure is 4 atmosphere. Density of kerosene oil = 0.72 kg /lite.

Explanation

To solve the problem of calculating the speed of efflux of kerosene oil from an orifice in a tank under a pressure of 4 atmospheres, we can follow these steps:

### Step 1: Convert the Pressure from Atmospheres to Pascals
The pressure given is 4 atmospheres. We need to convert this to pascals (N/m²) for our calculations.

\[ 1 \text{ atm} = 1.013 \times 10^5 \text{ N/m}^2 \]
\[ \text{Pressure} = 4 \text{ atm} = 4 \times 1.013 \times 10^5 \text{ N/m}^2 = 4.052 \times 10^5 \text{ N/m}^2 \]

### Step 2: Convert the Density of Kerosene Oil
The density of kerosene oil is given as 0.72 kg/liter. We need to convert this to kg/m³.

\[ 1 \text{ liter} = 0.001 \text{ m}^3 \]
\[ \text{Density} = 0.72 \text{ kg/liter} = 0.72 \text{ kg} / 0.001 \text{ m}^3 = 720 \text{ kg/m}^3 \]

### Step 3: Apply Bernoulli's Equation
We will use Bernoulli's equation to find the speed of efflux. The relevant form of Bernoulli's equation for this scenario is:

\[ P = \frac{1}{2} \rho v^2 \]

Where:
- \( P \) is the pressure (in N/m²),
- \( \rho \) is the density (in kg/m³),
- \( v \) is the velocity (in m/s).

### Step 4: Rearranging the Equation to Solve for Velocity
Rearranging the equation to solve for \( v \):

\[ v^2 = \frac{2P}{\rho} \]
\[ v = \sqrt{\frac{2P}{\rho}} \]

### Step 5: Substitute the Values into the Equation
Substituting the values we have:

\[ P = 4.052 \times 10^5 \text{ N/m}^2 \]
\[ \rho = 720 \text{ kg/m}^3 \]

Now, substituting these values into the equation for \( v \):

\[ v = \sqrt{\frac{2 \times 4.052 \times 10^5}{720}} \]

### Step 6: Calculate the Velocity
Calculating the above expression:

1. Calculate \( 2 \times 4.052 \times 10^5 = 8.104 \times 10^5 \).
2. Divide by 720:
\[ \frac{8.104 \times 10^5}{720} \approx 1126.39 \]
3. Take the square root:
\[ v \approx \sqrt{1126.39} \approx 33.55 \text{ m/s} \]

### Final Answer
The speed of efflux of kerosene oil from the orifice is approximately **33.55 m/s**.

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