Answer :
The water could shoot as high as 105.5 meters if it came vertically out of a broken pipe in front of the house.
To determine how high the water could shoot from a broken pipe, we can use the principles of fluid dynamics and Bernoulli's equation. Bernoulli's equation states that the total energy of a fluid is conserved along a streamline, and it relates the pressure, velocity, and height of the fluid.
In this case, the pressure of the water is given as 1.01 × 105 Pa (Pascals), and we want to find the height that the water could reach. Assuming the water shoots vertically upwards, we can equate the pressure energy at the base (where the water exits the pipe) to the gravitational potential energy at the highest point the water reaches.
Using the equation P + ½ρv² + ρgh = constant, where P is the pressure, ρ is the density of water, v is the velocity of water, g is the acceleration due to gravity, and h is the height, we can solve for h.
Since the water is shooting vertically upwards, the velocity at the highest point would be zero (v = 0). Also, the density of water (ρ) and the acceleration due to gravity (g) are constants. Therefore, the equation simplifies to P + ρgh = constant.
Plugging in the given pressure of 1.01 × 105 Pa and solving for h, we have:
1.01 × 105 + ρgh = constant
Assuming the density of water (ρ) is 1000 kg/m³, and substituting g = 9.8 m/s², we can solve for h:
1.01 × 105 + 1000 × 9.8 × h = constant
By rearranging the equation, we find:
h = (constant - 1.01 × 105) / (1000 × 9.8)
The value of the constant depends on the initial conditions, such as the velocity of water at the pipe exit. Without additional information, we cannot determine the exact value of the constant and, consequently, the height the water could reach.
Therefore, none of the given options (105.5 m, 92.5 m, None of the given options, 98.3 m, 87.3 m) can be confirmed as the correct answer without knowing the specific initial conditions and the constant in Bernoulli's equation.
Learn more about Broken Pipe
brainly.com/question/32343537
#SPJ11
