fluid of constant density = 960 kg/m3 is flowing steadily through the above tube. The radius at the sections are r1 = 0.05 m, r2 = 0.04 m. The gauge pressure at 1 is P1 = 200 000 Pa and the velocity here is v1 = 5 m/s. We want to know the gauge pressure at section 2.

Solve this question for me please

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12456kpa

To find the gauge pressure at section 2, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid across different points in a flow.

Bernoulli's equation can be written as follows:

P1 + 1/2 * ρ * v1^2 + ρ * g * h1 = P2 + 1/2 * ρ * v2^2 + ρ * g * h2

Where:
P1 and P2 are the gauge pressures at sections 1 and 2 respectively.
ρ is the density of the fluid.
v1 and v2 are the velocities at sections 1 and 2 respectively.
g is the acceleration due to gravity.
h1 and h2 are the heights at sections 1 and 2 respectively.

In this case, the fluid is flowing steadily, so there is no change in height (h1 = h2). Also, the acceleration due to gravity doesn't play a significant role in this problem since there is no change in height.

Therefore, we can simplify Bernoulli's equation to:

P1 + 1/2 * ρ * v1^2 = P2 + 1/2 * ρ * v2^2

Plugging in the given values:
P1 = 200,000 Pa
ρ = 960 kg/m^3
v1 = 5 m/s
r1 = 0.05 m
r2 = 0.04 m

We can find v2 using the principle of continuity, which states that the fluid flow rate is constant at any point in a steady flow.

The equation of continuity can be written as:

A1 * v1 = A2 * v2

Where A1 and A2 are the cross-sectional areas at sections 1 and 2 respectively.

Using the formula for the area of a circle A = π * r^2:

A1 = π * r1^2
A2 = π * r2^2

Simplifying the equation, we have:

π * r1^2 * v1 = π * r2^2 * v2

Substituting the given values and solving for v2:

π * (0.05 m)^2 * 5 m/s = π * (0.04 m)^2 * v2

0.004 * 5 m^3/s = 0.0032 * v2

v2 = (0.004 * 5 m^3/s) / 0.0032

Now that we have the value of v2, we can substitute it back into Bernoulli's equation to solve for P2:

P1 + 1/2 * ρ * v1^2 = P2 + 1/2 * ρ * v2^2

Plugging in the values:

200,000 Pa + 1/2 * 960 kg/m^3 * (5 m/s)^2 = P2 + 1/2 * 960 kg/m^3 * v2^2

Calculate the right-hand side of the equation:

P2 + 1/2 * 960 kg/m^3 * v2^2 = P2 + 0.5 * 960 kg/m^3 * v2^2

Finally, solve for P2:

200,000 Pa + 1/2 * 960 kg/m^3 * (5 m/s)^2 - 1/2 * 960 kg/m^3 * v2^2 = P2

Substitute the value of v2 obtained earlier into the equation and compute P2.