A team from Engineers Without Borders constructs a system to supply water to a mountainside village located 1800 m above sea level from a spring in the valley below at 1500 m above sea level. When the pipe from the spring to the village is full of water, but no water is flowing, what is the pressure difference between the end of the pipe at the ?spring and the end of the pipe in the village Given water density of water as 1000 kg/m
.and the acceleration of gravity as 9.8 m/s
???? ??? ???????? a. 14.5 bar b. 2940 kPa c. 29.4 bar d. 58.8 bar
A team from Engineers Without Borders constructs a system to supply water to a mountainside village located 1800 m above sea level from a spring in the valley below at 1500 m above sea level. When the pipe from the spring to the village is full of water, but no water is flowing, what is the pressure difference between the end of the pipe at the ?spring and the end of the pipe in the village Given water density of water as 1000 kg/m
.and the acceleration of gravity as 9.8 m/s
???? ??? ???????? a. 14.5 bar b. 2940 kPa c. 29.4 bar d. 58.8 bar
The Correct Answer and Explanation is:
Correct Answer: c. 29.4 bar
Explanation:
To find the pressure difference between the spring and the village when the pipe is full of water but no water is flowing (i.e., the system is in static equilibrium), we can use the hydrostatic pressure formula: ΔP=ρgh\Delta P = \rho g h
Where:
- ΔP\Delta P = pressure difference (Pa or N/m²)
- ρ\rho = density of water = 1000 kg/m³
- gg = acceleration due to gravity = 9.8 m/s²
- hh = vertical height difference = 1800 m – 1500 m = 300 m
ΔP=1000×9.8×300=2,940,000 Pa\Delta P = 1000 \times 9.8 \times 300 = 2,940,000 \text{ Pa}
Now convert Pascals to kilopascals (kPa): 2,940,000 Pa=2940 kPa2,940,000 \, \text{Pa} = 2940 \, \text{kPa}
Now convert kPa to bar, knowing that: 1 bar=100 kPa1 \, \text{bar} = 100 \, \text{kPa} ΔP=2940100=29.4 bar\Delta P = \frac{2940}{100} = 29.4 \, \text{bar}
Physical Interpretation:
This pressure difference arises purely due to the difference in elevation. Because the spring is 300 meters below the village, water in the vertical column between the spring and the village creates a hydrostatic pressure. Since water is incompressible, the pressure at the bottom (spring) is higher than at the top (village) by the amount calculated.
In real-world applications, this principle is vital in gravity-fed water systems, where elevation differences allow water to flow without the need for pumps. When there’s no flow, the water simply exerts pressure due to its own weight, which is directly proportional to the height of the water column.
This scenario assumes no friction losses or atmospheric pressure differences, as it’s strictly a static case.
