Respuesta :
Answer:
Gauge Pressure = 127.4 KPa
Explanation:
From Bernoulli equation, we know that;
P1 + ρ•g•y1 + (1/2)ρ(v_1)² = P2 + ρ•g•y2 + (1/2)ρ(v_2)²
We will set our initial height as 0m and final height as 13m
Also, the question says that the mains have a much larger diameter than the hose. Thus, we can say that v_1 ≈ 0
Furthermore, once the water reaches its altitude of 13m,it stops going higher. Thus, v2 would also be 0.
Now, to simplify the Bernoulli equation further, and given that we are solving for gauge pressure, we can say that the pressure at the top of our column of water is zero, since we need to know the amount of pressure to shoot the water that high in the air anyway. So, P2 =0
Thus, when we plug in the relevant values into the Bernoulli equation written earlier, we arrive at;
P1 = ρ•g•y2
Density of water = 100 kg/m³
So, P1 = 1000 x 9.8 x 13 = 127,400 Pa = 127.4 KPa
When the city water mains for a stream from a fire hose connected to the mains reach a vertical height of 13.0 m Gauge Pressure is = 127.4 KPa
What is the Bernoulli equation?
From the Bernoulli equation, we understand that;
P1 + ρ•g•y1 + (1/2)ρ(v_1)² = P2 + ρ•g•y2 + (1/2)ρ(v_2)²
We will set our initial height as 0m and final height as 13m
Also, the inquiry says that the mains have a much larger diameter than the hose. Thus, we can say that v_1 ≈ 0
Again, once the water reaches its altitude of 13m, it stops moving higher. Thus, v2 would also be 0.
Now, to facilitate the Bernoulli equation differently, and given that we are solving for gauge force, we can say that the pressure at the top of our column of water is zero
since we require to know the amount of pressure to shoot the water that high in the air anyway. So, P2 is =0
Therefore, when we plug in the appropriate values into the Bernoulli equation written prematurely, we arrive at;
P1 = ρ•g•y2
Density of water is = 100 kg/m³
Hence, P1 = 1000 x 9.8 x 13 = 127,400 Pa = 127.4 KPa
Find more information about Bernoulli equation here:
https://brainly.com/question/14082066
