A1,A2 The image displays a mathematical equation used in fluid dynamics or related fields to determine the velocity of a gas under specific conditions. The equation is:\[ V_2 = \left[ \dfrac{2RT_1}{P_1M} (P_1 - P_{\text{atm}}) \right]^{1/2} \]Where:- \( V_2 \) is the velocity of the gas.- \( R \) is the ideal gas constant.- \( T_1 \) is the initial temperature.- \( P_1 \) is the initial pressure of the gas.- \( P_{\text{atm}} \) is the atmospheric pressure.- \( M \) is the molar mass of the gas.This formula is typically used to understand how pressure, temperature, and specific gas properties affect gas velocity in scenarios such as vents, exhausts, or nozzles. ### Problem StatementA tank is full of water and open at the top, as illustrated in the figure. There is a frictionless nozzle near the bottom, the diameter of which is small compared with the diameter of the tank. Assuming the flow is steady:1. **What is the velocity of the flow out of the nozzle?** \[ V_2 = \sqrt{2gh \left(1 - \frac{\rho_{\text{air}}}{\rho_{\text{fluid}}}\right) \left(\frac{1}{1 - \left(\frac{A_2}{A_t}\right)^2}\right)} \] - **\(d_1 > d_2\):** This indicates that the diameter of the tank \(d_1\) is greater than the diameter of the nozzle \(d_2\). - **\(g = 9.81 \, \text{m/s}^2\):** This is the acceleration due to gravity. 2. **If the tank is full of CO2, what is the velocity of the flow out of the nozzle?**### Explanation of Diagram- The diagram shows a vertical tank filled with water. The height of the water column is \(h = 10 \, \text{m}\).- There is an illustration of a nozzle at the bottom right of the tank, labeled "Tank draining," indicating the water flow direction.- The diagram includes two points: - Point \(1\) marks the top surface of the water. - Point \(2\) marks the exit point of the nozzle, showing the flow of water out of the tank.### ApplicationThe formula provided is derived from Bernoulli's principle, accounting for the density of the fluid and the effects of gravity. The equation can be used to determine the velocity of fluid flowing out of a nozzle, given a height difference and fluid characteristics, such as when the tank is filled with a different fluid like CO2.

Solution: Given Data: z1 = 10 m P1=P2=PatmV1=0z2=0

4. A tank is full of water and open at the top as shown in the figure. There is a frictionless nozzle near the bottom, the diameter of which is small compared with the diameter of the tank. Assuming the flow is steady, (1) What is the velocity of the flow out of the nozzle? ( d₁ > d₂ V₂ = 12gh (1-Pair (@Aluid) 1 ² g=9.812/23 h-10 m (2) If the tank is full of CO2, what is the velocity of the flow out of the nozzle? Tank draining

4. A tank is full of water and open at the top as shown in the figure. There is a frictionless nozzle near the bottom, the diameter of which is small compared with the diameter of the tank. Assuming the flow is steady, (1) What is the velocity of the flow out of the nozzle? ( d₁ > d₂ V₂ = 12gh (1-Pair (@Aluid) 1 ² g=9.812/23 h-10 m (2) If the tank is full of CO2, what is the velocity of the flow out of the nozzle? Tank draining

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

A1,A2

The image displays a mathematical equation used in fluid dynamics or related fields to determine the velocity of a gas under specific conditions. The equation is:

\[ V_2 = \left[ \dfrac{2RT_1}{P_1M} (P_1 - P_{\text{atm}}) \right]^{1/2} \]

Where:
- \( V_2 \) is the velocity of the gas.
- \( R \) is the ideal gas constant.
- \( T_1 \) is the initial temperature.
- \( P_1 \) is the initial pressure of the gas.
- \( P_{\text{atm}} \) is the atmospheric pressure.
- \( M \) is the molar mass of the gas.

This formula is typically used to understand how pressure, temperature, and specific gas properties affect gas velocity in scenarios such as vents, exhausts, or nozzles.

### Problem Statement

A tank is full of water and open at the top, as illustrated in the figure. There is a frictionless nozzle near the bottom, the diameter of which is small compared with the diameter of the tank. Assuming the flow is steady:

1. **What is the velocity of the flow out of the nozzle?**

\[
V_2 = \sqrt{2gh \left(1 - \frac{\rho_{\text{air}}}{\rho_{\text{fluid}}}\right) \left(\frac{1}{1 - \left(\frac{A_2}{A_t}\right)^2}\right)}
\]

- **\(d_1 > d_2\):** This indicates that the diameter of the tank \(d_1\) is greater than the diameter of the nozzle \(d_2\).
- **\(g = 9.81 \, \text{m/s}^2\):** This is the acceleration due to gravity.

2. **If the tank is full of CO2, what is the velocity of the flow out of the nozzle?**

### Explanation of Diagram

- The diagram shows a vertical tank filled with water. The height of the water column is \(h = 10 \, \text{m}\).
- There is an illustration of a nozzle at the bottom right of the tank, labeled "Tank draining," indicating the water flow direction.
- The diagram includes two points:
- Point \(1\) marks the top surface of the water.
- Point \(2\) marks the exit point of the nozzle, showing the flow of water out of the tank.

### Application

The formula provided is derived from Bernoulli's principle, accounting for the density of the fluid and the effects of gravity. The equation can be used to determine the velocity of fluid flowing out of a nozzle, given a height difference and fluid characteristics, such as when the tank is filled with a different fluid like CO2.

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