does it take more pressure to push water up a vertical pipe than the same pipe on a 45 degree incline
To determine whether it takes more pressure to push water up a vertical pipe compared to the same pipe on a 45-degree incline, we can analyze the forces involved.
When the water flows through a pipe, the pressure is responsible for pushing the water. This pressure is created by the height of the water column above a certain point, known as the "head pressure." The pressure can be calculated using the equation P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column.
In both cases, the height of the water column is the same; it only depends on the vertical distance from the water source to the point in the pipe under consideration. Therefore, the head pressure would be the same for both the vertical pipe and the 45-degree inclined pipe.
However, when the pipe is inclined, there is an additional force acting against the flow of water: gravity. Gravity pulls the water downwards due to its vertical component, opposing the flow. On a steeper incline, such as a vertical pipe, gravity acts more strongly against the water flow, requiring additional pressure to overcome it and push the water up the pipe.
Therefore, it takes more pressure to push water up a vertical pipe compared to the same pipe on a 45-degree incline, due to the additional force of gravity acting against the flow of water.