(3) The geyser "Old Faithful" in Yellowstone National Park rises about 32 m upon eruption. Estimate the velocity of the water at the ground surface.
(3) The geyser "Old Faithful" in Yellowstone National Park rises about 32 m upon eruption. Estimate the velocity of the water at the ground surface.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Please answer question 3 asap
![**Sample Datasheet**
**(2) A water main on Warren Street suddenly springs a leak, and you estimate the geyser reaches about 20 feet in height. You further estimate that about 300 gallons per minute is leaking based on the water flowing in the gutter. About how big is the hole in the water pipe?**
The problem begins by considering a water pipe with a leak, forming a geyser:
\[ z_1, V_1, P_1 \]
\[ z_2, V_2, P_2 \]
Applying Bernoulli’s equation:
\[ z_1 + \frac{V_1^2}{2g} + \frac{P_1}{\rho g} = z_2 + \frac{V_2^2}{2g} + \frac{P_2}{\rho g} \]
Simplifying:
\[ \frac{P_2 - P_1}{\rho g} + \frac{V_2^2 - V_1^2}{2g} + z_2 - z_1 = 0 \]
Assuming \( V_1 \approx 0 \) and rearranging gives:
\[ V_2 = \sqrt{2 g h} \]
Substituting \( h = 6 \) m:
\[ V_2 = \sqrt{2 \times 9.81 \times 6.096} = 10.94 \, \text{m/s} \]
For the area of the hole:
\[ A = \frac{Q}{V_2} = \frac{0.0189}{10.94} = 1.73 \times 10^{-3} \, \text{m}^2 \]
Using the formula for the area of a circle, \( \frac{\pi D^2}{4} \):
\[ 1.73 \times 10^{-3} = \frac{\pi D^2}{4} \]
Solving for the diameter:
\[ D = 0.469 \, \text{m} = 4.69 \, \text{cm} \]
**(3) The geyser “Old Faithful” in Yellowstone National Park rises about 32 m upon eruption. Estimate the velocity of the water at the ground surface.**
For Old Faithful:
Applying the energy equation similar to the leak problem, the potential](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb0db590-5d37-48a1-bf5a-623f4987797d%2F3a5a000f-0b7e-4bbe-893a-de81a1a8d8ae%2Fui12dqd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Sample Datasheet**
**(2) A water main on Warren Street suddenly springs a leak, and you estimate the geyser reaches about 20 feet in height. You further estimate that about 300 gallons per minute is leaking based on the water flowing in the gutter. About how big is the hole in the water pipe?**
The problem begins by considering a water pipe with a leak, forming a geyser:
\[ z_1, V_1, P_1 \]
\[ z_2, V_2, P_2 \]
Applying Bernoulli’s equation:
\[ z_1 + \frac{V_1^2}{2g} + \frac{P_1}{\rho g} = z_2 + \frac{V_2^2}{2g} + \frac{P_2}{\rho g} \]
Simplifying:
\[ \frac{P_2 - P_1}{\rho g} + \frac{V_2^2 - V_1^2}{2g} + z_2 - z_1 = 0 \]
Assuming \( V_1 \approx 0 \) and rearranging gives:
\[ V_2 = \sqrt{2 g h} \]
Substituting \( h = 6 \) m:
\[ V_2 = \sqrt{2 \times 9.81 \times 6.096} = 10.94 \, \text{m/s} \]
For the area of the hole:
\[ A = \frac{Q}{V_2} = \frac{0.0189}{10.94} = 1.73 \times 10^{-3} \, \text{m}^2 \]
Using the formula for the area of a circle, \( \frac{\pi D^2}{4} \):
\[ 1.73 \times 10^{-3} = \frac{\pi D^2}{4} \]
Solving for the diameter:
\[ D = 0.469 \, \text{m} = 4.69 \, \text{cm} \]
**(3) The geyser “Old Faithful” in Yellowstone National Park rises about 32 m upon eruption. Estimate the velocity of the water at the ground surface.**
For Old Faithful:
Applying the energy equation similar to the leak problem, the potential
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