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Answer :
To determine how far the water would travel if the hose were pointed straight upward, follow these steps:
1. Understand the given pressure:
- The water is supplied at a pressure of 30 psig (pounds per square inch gauge).
2. Convert gauge pressure to absolute pressure:
- Gauge pressure (psig) measures pressure relative to atmospheric pressure. To convert it to absolute pressure (psia), we add atmospheric pressure, which is about 14.7 psi.
- Therefore, the absolute pressure is: 30 psig + 14.7 psi = 44.7 psia.
3. Convert pressure to pascals:
- Pressure in psi can be converted to pascals using the conversion factor: 1 psi = 6894.76 pascals.
- So, the pressure in pascals is: 44.7 psia * 6894.76 = 308195.772 pascals.
4. Calculate the maximum height the water can reach:
- Use the formula for maximum height (h) achieved by a fluid due to pressure:
[tex]\[
h = \frac{\text{pressure (in pascals)}}{\text{density of water} \times g}
\][/tex]
where the density of water is approximately 1000 kg/m³, and g (acceleration due to gravity) is 9.81 m/s².
- Plug in the values to calculate the height:
[tex]\[
h = \frac{308195.772 \, \text{pascals}}{1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2} \approx 31.42 \, \text{meters}
\][/tex]
Therefore, under ideal conditions with no air resistance or other losses, the water would travel approximately 31.42 meters upward.
1. Understand the given pressure:
- The water is supplied at a pressure of 30 psig (pounds per square inch gauge).
2. Convert gauge pressure to absolute pressure:
- Gauge pressure (psig) measures pressure relative to atmospheric pressure. To convert it to absolute pressure (psia), we add atmospheric pressure, which is about 14.7 psi.
- Therefore, the absolute pressure is: 30 psig + 14.7 psi = 44.7 psia.
3. Convert pressure to pascals:
- Pressure in psi can be converted to pascals using the conversion factor: 1 psi = 6894.76 pascals.
- So, the pressure in pascals is: 44.7 psia * 6894.76 = 308195.772 pascals.
4. Calculate the maximum height the water can reach:
- Use the formula for maximum height (h) achieved by a fluid due to pressure:
[tex]\[
h = \frac{\text{pressure (in pascals)}}{\text{density of water} \times g}
\][/tex]
where the density of water is approximately 1000 kg/m³, and g (acceleration due to gravity) is 9.81 m/s².
- Plug in the values to calculate the height:
[tex]\[
h = \frac{308195.772 \, \text{pascals}}{1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2} \approx 31.42 \, \text{meters}
\][/tex]
Therefore, under ideal conditions with no air resistance or other losses, the water would travel approximately 31.42 meters upward.
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