Question

2008B4 a drinking fountain c) The fountain is fed by a pipe that at one point has a radius of 7.00 x 10 m and is 3.00 m below the fountain's opening. The density of water is 1.0 x 10 kg/m. Calculate the gauge pressure in the feeder pipe at this point.

Answer 1

The gauge pressure in the feeder pipe below the drinking fountain's opening can be found using the hydrostatic pressure formula. With the water density of 1.0 x 10^3 kg/m^3 and a height difference of 3.00 m, the calculated gauge pressure is 2.943 x 10^4 Pa.

Step-by-step explanation:

The question involves calculating the gauge pressure in the feeder pipe that supplies water to a drinking fountain. This calculation requires an understanding of fluid mechanics, which is a branch of physics. To find the gauge pressure at a point in the pipe, we apply the hydrostatic pressure formula, which states that the pressure due to a fluid at a certain depth is proportional to the density of the fluid, the gravitational acceleration, and the depth itself. Using the given values:

• Density of water (ρ) = 1.0 x 103 kg/m3
• Gravitational acceleration (g) = 9.81 m/s2
• Height difference (h) = 3.00 m

Here is the calculation:

Pgauge = ρgh = (1.0 x 103 kg/m3)(9.81 m/s2)(3.00 m) = 2.943 x 104 Pa

The gauge pressure at the point in the feeder pipe is 2.943 x 104 Pascals (Pa).