**Calculation of Pressure at the Smaller Diameter**

To calculate the pressure at the smaller diameter of the pipe, we can use the principle of continuity equation and Bernoulli's equation.

**1. Continuity Equation:**
The continuity equation states that the mass flow rate of a fluid remains constant in an incompressible flow. Mathematically, it can be expressed as:

A1v1 = A2v2

where A1 and A2 are the cross-sectional areas of the pipe at the larger and smaller diameters, respectively, and v1 and v2 are the velocities of the fluid at those points.

**2. Bernoulli's Equation:**
Bernoulli's equation relates the pressure, velocity, and elevation of a fluid in a streamline. Mathematically, it can be expressed as:

P1 + 0.5ρv1^2 + ρgh1 = P2 + 0.5ρv2^2 + ρgh2

where P1 and P2 are the pressures at the larger and smaller diameters, respectively, ρ is the density of the fluid, g is the acceleration due to gravity, and h1 and h2 are the elevations at those points.

**3. Solving the Equations:**
Let's assume the velocity at the larger diameter (v1) is unknown and the velocity at the smaller diameter (v2) is also unknown. We need to find both of these values.

We are given the following information:
- Diameter at the larger end (D1) = 100 mm = 0.1 m
- Diameter at the smaller end (D2) = 60 mm = 0.06 m
- Incline angle (θ) = 15 degrees
- Pressure at the larger diameter (P1) = 2.3 bar = 2.3 x 105 Pa
- Mass flow rate (m) = 20 tons per hour = 20 x 1000 kg/h = (20 x 1000) / 3600 kg/s

**4. Calculating Cross-sectional Areas:**
The cross-sectional areas can be calculated using the formula for the area of a circle:

A = πr^2

where r is the radius of the pipe.

- Area at the larger end (A1) = π(0.05)^2
- Area at the smaller end (A2) = π(0.03)^2

**5. Calculating Velocities:**
Using the continuity equation, we can find the velocity at the smaller diameter (v2):

A1v1 = A2v2

v2 = (A1v1) / A2

**6. Calculating Velocity at the Larger Diameter:**
To find the velocity at the larger diameter (v1), we can use the elevation difference between the two points.

h1 - h2 = 10m x sin(15 degrees)

**7. Plugging Values into Bernoulli's Equation:**
Using Bernoulli's equation, we can substitute the known values:

P1 + 0.5ρv1^2 + ρgh1 = P2 + 0.5ρv2^2 + ρgh2

**8. Solving the Equations:**
Now, we can solve the equations simultaneously to find the velocity at the larger diameter (v1