Question

At one place the pressure is 130 kPa and the speed is 0.6 m/s. Determine the pressure at another place in the same pipe where the speed is 9 m/s.​

Answer 1

The answer is 90 kPa, assuming that water is flowing steadily through a horizontal pipe of varying cross-section.

Answer 2

To solve this problem, we can use the Bernoulli's principle which states that the total mechanical energy of a fluid flowing along a streamline is constant, ignoring dissipative forces like friction. Mathematically, this can be expressed as:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

where P1 and v1 are the pressure and speed at one place, P2 and v2 are the pressure and speed at another place, and ρ is the density of the fluid.

We can rearrange the equation to solve for P2:

P2 = P1 + (1/2)ρ(v1^2 - v2^2)

Substituting the given values, we get:

P2 = 130 kPa + (1/2)(1.2 kg/m^3)(0.6 m/s)^2 - (1/2)(1.2 kg/m^3)(9 m/s)^2

P2 = 130 kPa + 0.216 kPa - 5.832 kPa

P2 = 124.384 kPa

Therefore, the pressure at the other place in the same pipe where the speed is 9 m/s is approximately 124.384 kPa.