Final answer:
To find the pressure at the higher end of a pipe using Bernoulli's equation, subtract the hydrostatic pressure difference caused by the elevation change from the initial pressure at the lower end, considering the fluid density and gravity.
Step-by-step explanation:
The question asked is regarding the change in pressure of water as it flows through a pipe with a change in height, which is a concept from fluid dynamics in physics. To calculate the pressure at the other end, one can apply Bernoulli's equation, which states that for an incompressible, non-viscous fluid, the sum of pressure energy, kinetic energy, and potential energy per unit volume is constant along a streamline. Given that water flows at 5 m/s with a pressure of 1.5 x 10⁵ Pa at the lower end and the other end is 12 m higher, the pressure at the upper end will be the initial pressure minus the hydrostatic pressure difference due to the change in elevation. Ignoring the frictional losses, and assuming constant flow speed, the pressure at the upper end is given by:
P₁ + ½ρv² + ρgh₁ = P₂ + ½ρv² + ρgh₂
Where ρ is the density of water, g is the acceleration due to gravity, h is height, P is pressure, and v is the flow velocity. The decrease in pressure at the upper end due to the height difference is ρgh, which can be calculated using the values for the density of water (approximately 1000 kg/m³), g (9.81 m/s²), and the height difference (12 m). Subtracting this hydrostatic pressure difference from the initial pressure gives the pressure at the upper end.