water is flowing through a horizontal pipe of varying cross section at any two places the diameters of the tube are 4cm and 2cm if the pressure difference between these

To find the pressure difference between the two places in the pipe where the diameters are 4cm and 2cm, you need to use the principles of fluid dynamics.

The Bernoulli's equation can help us solve this problem. The Bernoulli's equation states that the sum of the pressure head, the kinetic head, and the potential head of a fluid remains constant along a streamline. For horizontal pipe flow, we can neglect the potential head since the elevations are the same.

The pressure head can be represented by the formula:

P₁/ρg + (v₁²/2g) + z₁ = P₂/ρg + (v₂²/2g) + z₂

Where:
- P₁ and P₂ are the pressures at the two different cross-sections,
- ρ is the density of water,
- g is the acceleration due to gravity,
- v₁ and v₂ are the velocities of water at the two cross-sections, and
- z₁ and z₂ are the heights of the locations of the two cross-sections.

Since the pipe is horizontal, the heights (z₁ and z₂) will be the same.

The velocity of water can be calculated using the equation:

A₁v₁ = A₂v₂

Where:
- A₁ and A₂ are the areas of the cross-sections at the two points.

Given that the diameter of the first cross-section is 4cm, we can calculate A₁ as:

A₁ = π (d₁/2)²

Given that the diameter of the second cross-section is 2cm, we can calculate A₂ as:

A₂ = π (d₂/2)²

Substituting these values into the equation above, we can find v₁ and v₂.

Once you have the velocities and the height, you can use the Bernoulli's equation to find the pressure difference between the two locations in the pipe.

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