1. The system in right figure consists of a water reservoir with a layer of compressed air above the water and a large pipe and nozzle. The pressure of the air is 50 psig, and the effects of friction can be neglected. What is the velocity of the water flowing out through the nozzle? 50 psig 30 ft

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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1. The system in right figure consists of a water reservoir with a
layer of compressed air above the water and a large pipe and nozzle.
The pressure of the air is 50 psig, and the effects of friction can be
neglected. What is the velocity of the water flowing out through the
nozzle?
50 psig
2. The tank in right figure is cylindrical and has a vertical axis. Its
horizontal cross-sectional area is 100 ft². The hole in the bottom has
a cross-sectional area of 1 ft². The interface between the gasoline and the
water remains perfectly horizontal at all times. That interface is now 10 ft
above the bottom. How soon will gasoline start to flow out the bottom?
Assume frictionless flow.
30 ft
10 ft
10 ft
1
Gasoline
Water
iiili
Transcribed Image Text:1. The system in right figure consists of a water reservoir with a layer of compressed air above the water and a large pipe and nozzle. The pressure of the air is 50 psig, and the effects of friction can be neglected. What is the velocity of the water flowing out through the nozzle? 50 psig 2. The tank in right figure is cylindrical and has a vertical axis. Its horizontal cross-sectional area is 100 ft². The hole in the bottom has a cross-sectional area of 1 ft². The interface between the gasoline and the water remains perfectly horizontal at all times. That interface is now 10 ft above the bottom. How soon will gasoline start to flow out the bottom? Assume frictionless flow. 30 ft 10 ft 10 ft 1 Gasoline Water iiili
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can u explain to me why this solution isnt correct?

The text presents a fluid mechanics problem involving Bernoulli’s equation:

1. **Initial Assumptions:**
   - The system is open to the atmosphere, so \( P_1 = P_2 = 0 \).
   - The inlet velocity (\( V_{\text{inlet}} \)) is 0 and is not provided.

2. **Bernoulli's Equation:**
   \[
   \frac{P_1}{\rho} + gz_1 + \frac{V_1^2}{2} = \frac{P_2}{\rho} + gz_2 + \frac{V_2^2}{2} + F_{\text{friction}}
   \]
   - Friction term (\( F_{\text{friction}} \)) is crossed out, indicating negligible friction.

3. **Simplified Equation:**
   \[
   \left(\frac{P_2 - P_1}{\rho}\right) + \left(\frac{V_2^2 - V_1^2}{2}\right) + g(z_2 - z_1) = 0
   \]
   - The terms \(\frac{V_2^2}{2} + g(z_2 - z_1) = 0\) further simplify the equation.

4. **Final Velocity Derivation:**
   \[
   \frac{V_2^2}{2} = gz_1 \quad \text{where} \quad z_1 = 10 \text{ ft}
   \]
   - Velocity calculation for water (\( V_2 \)):
   \[
   V_2(\text{water}) = \sqrt{2gz_1} = \sqrt{\frac{32.2 \text{ ft/s}^2 \times 20 \text{ ft}}{2}} = 25.38 \text{ ft/s}
   \]
   The final velocity of the water is 25.38 feet per second.
Transcribed Image Text:The text presents a fluid mechanics problem involving Bernoulli’s equation: 1. **Initial Assumptions:** - The system is open to the atmosphere, so \( P_1 = P_2 = 0 \). - The inlet velocity (\( V_{\text{inlet}} \)) is 0 and is not provided. 2. **Bernoulli's Equation:** \[ \frac{P_1}{\rho} + gz_1 + \frac{V_1^2}{2} = \frac{P_2}{\rho} + gz_2 + \frac{V_2^2}{2} + F_{\text{friction}} \] - Friction term (\( F_{\text{friction}} \)) is crossed out, indicating negligible friction. 3. **Simplified Equation:** \[ \left(\frac{P_2 - P_1}{\rho}\right) + \left(\frac{V_2^2 - V_1^2}{2}\right) + g(z_2 - z_1) = 0 \] - The terms \(\frac{V_2^2}{2} + g(z_2 - z_1) = 0\) further simplify the equation. 4. **Final Velocity Derivation:** \[ \frac{V_2^2}{2} = gz_1 \quad \text{where} \quad z_1 = 10 \text{ ft} \] - Velocity calculation for water (\( V_2 \)): \[ V_2(\text{water}) = \sqrt{2gz_1} = \sqrt{\frac{32.2 \text{ ft/s}^2 \times 20 \text{ ft}}{2}} = 25.38 \text{ ft/s} \] The final velocity of the water is 25.38 feet per second.
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