Question

water is circulating through a closed system of pipes in a two floor apartment. on the first floor, the water has a gauge pressure of 3.30 105 pa and a speed of 2.2 m/s. however, on the second floor, which is 3.7 m higher, the speed of the water is 4.1 m/s. the speeds are different because the pipe diameters are different. what is the gauge pressure of the water on the second floor?

Answer 1

The gauge pressure of water on the second floor of the apartment can be determined using Bernoulli's principle.

Step-by-step explanation:

To answer this question, we need to use Bernoulli's principle, which states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. In the context of the apartment, the water on the second floor is moving faster and at a higher elevation, thus would have a lower gauge pressure compared to the first floor due to energy conservation.

Firstly, note that gauge pressure is the pressure relative to atmospheric pressure. Therefore, we can use Bernoulli's equation for both floors:

For the first floor: P1 + 0.5*ρ*v1^2 + ρ*g*h1 = Constant

For the second floor: P2 + 0.5*ρ*v2^2 + ρ*g*h2 = Constant

Where P1 and P2 are the pressures on the first and second floor respectively, ρ is the density of the water, v1 and v2 are the speeds of the water on the first and second floor, g is the acceleration due to gravity, and h1 and h2 are the heights on the first and second floor respectively.

Setting the two equations equal to one another (as the Constant must be the same) and solving for P2, we can calculate the gauge pressure on the second floor.

Learn more about Bernoulli's Principle