Final answer:
The original speed of the water entering the pipe can be calculated using Bernoulli's equation, which relates the pressure, velocity, and height of a flowing fluid at two points. This involves using the known pressure, speed, and height changes between the bottom and the top of the pipe.
Step-by-step explanation:
To determine the original speed at which the water was moving into the pipe, we can use the Bernoulli's equation which relates the speed of a fluid, its pressure, and its height at two different points along its flow. According to Bernoulli's principle, the total mechanical energy (including kinetic energy from the velocity of the water, gravitational potential energy from the height, and the energy from the pressure) is constant as the water flows, assuming there's no energy loss due to factors like friction.
Bernoulli's equation is written as:
P1 + 0.5∙ρ∙v12 + ρ∙g∙h1 = P2 + 0.5∙ρ∙v22 + ρ∙g∙h2
Where:
- P1 and P2 are the pressures at the bottom and top of the pipe, respectively.
- ρ is the density of water (assumed to be 1000 kg/m3 for pure water).
- g is the acceleration due to gravity (9.81 m/s2).
- v1 and v2 are the velocities of water at the bottom and top of the pipe, respectively.
- h1 and h2 are the heights of the pipe at the bottom and top, respectively.
We will solve for v1 knowing P1 = 11,962 Pa, P2 = 10,037 Pa, v2 = 3.3 m/s and h2 - h1 = 1.6 m.
Plugging in the values into Bernoulli's equation and solving for v1:
11,962 Pa + 0.5∙(1000 kg/m3)∙v12 + (1000 kg/m3)∙(9.81 m/s2)∙(0 m) = 10,037 Pa + 0.5∙(1000 kg/m3)∙(3.3 m/s)2 + (1000 kg/m3)∙(9.81 m/s2)∙(1.6 m)
Upon simplifying the equation and solving for v1, you'll find the speed at which the water originally entered the pipe.