Question

if the initial velocity of a fluid is 5m/s and final velocity is 10m/s the initial pressure is 110 kpa within un changing potential energy what is the value of pressure?​

Answer 1

To find the final pressure of a fluid with an initial pressure of 110 kPa and given velocities, we can use Bernoulli's equation. Plugging in the values, the final pressure is calculated to be 87.5 kPa.

Step-by-step explanation:

To find the final pressure of a fluid with an initial pressure of 110 kPa, we need to use Bernoulli's equation. Bernoulli's equation relates the initial and final velocities and pressures of a fluid.

In this case, the initial velocity of the fluid is 5 m/s and the final velocity is 10 m/s. Let's assume that the potential energy remains unchanged.

Using Bernoulli's equation:

P1 + ½ρv12 = P2 + ½ρv22

Where P1 and P2 are the initial and final pressures respectively, and v1 and v2 are the initial and final velocities respectively.

Plugging in the values:

110 + ½(π*1.2*52) = P2 + ½(π*1.2*102)

Simplifying the equation:

110 + 7.5 = P2 + 30

P2 = 110 + 7.5 - 30

P2 = 87.5 kPa

Answer 2

The value of pressure, assuming unchanging potential energy, is 95 kPa.

Step-by-step explanation:

To find the value of pressure, we can use Bernoulli's equation, which states that the total energy of a fluid particle is conserved in the absence of external work. The equation is
`\(P + (1)/(2)\rho v^2 + \rho gh = \text{constant}\)`, where P is the pressure,
`\(\rho\)` is the density of the fluid, v is the velocity, g is the acceleration due to gravity, and h is the height.

Since the potential energy is unchanging, the term
`\(\rho gh\)` remains constant. As the fluid speeds up from an initial velocity of 5 m/s to a final velocity of 10 m/s, the pressure decreases. The final pressure can be calculated by rearranging the Bernoulli's equation and substituting the given values.

The final pressure is found to be 95 kPa, reflecting the decrease in pressure as the fluid's velocity increases.