Question

in the horizontal pipe there is liquid that is flowing and the pipe involved gradually converge from a diameter of 200cm at position A to 150cm at position B. if the velocity at A is 2m/s and the pressure head at B take (g=10ms and Z as the datum​

Answer 1

Step-by-step explanation:

To determine the velocity and pressure head at position B in a horizontally converging pipe, we can use the principle of conservation of mass and Bernoulli's equation.

According to the principle of conservation of mass, the mass flow rate remains constant throughout the pipe. Therefore, we can write:

A₁V₁ = A₂V₂

where A₁ and A₂ are the cross-sectional areas at positions A and B, respectively, and V₁ and V₂ are the velocities at positions A and B, respectively.

Given:

A₁ = (π/4)(d₁)² = (π/4)(200 cm)² = 31416 cm²

A₂ = (π/4)(d₂)² = (π/4)(150 cm)² = 17671 cm²

V₁ = 2 m/s

We can calculate V₂ using the equation:

V₂ = (A₁V₁) / A₂

Substituting the values:

V₂ = (31416 cm² * 2 m/s) / 17671 cm² ≈ 3.54 m/s

Therefore, the velocity at position B is approximately 3.54 m/s.

Next, to determine the pressure head at position B, we can use Bernoulli's equation:

P₁ + (1/2)ρV₁² + ρgh₁ = P₂ + (1/2)ρV₂² + ρgh₂

Assuming the datum is at position B, where the pressure head (h₂) is zero, the equation simplifies to:

P₁ + (1/2)ρV₁² + ρgh₁ = P₂ + (1/2)ρV₂²

Given:

g = 10 m/s² (acceleration due to gravity)

Z = 0 m (datum)

ρ = density of the liquid (not given)

Since the density (ρ) of the liquid is not provided, we cannot determine the absolute pressure at position B or calculate the pressure head. The information given is insufficient to determine the pressure head at position B.

In summary:

- The velocity at position B is approximately 3.54 m/s.

- The pressure head at position B cannot be determined with the given information.