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I took a flight from Los Angeles to Denver, and I carried with me a closed water bottle of the type that delivers water to me through a built-in straw (see Figure 1). The bottle has an internal diameter of D = 6 cm, and an internal height of H₂ = 25cm. It is A% filled with water. The straw tip (outlet)H = H₂ + 3cm. The last time I opened the bottle before I departed was at LAX, where the atmospheric pressure wasP = B hPa. While waiting for my ride at Denver International Airport, atmospheric pressure? = C hPa, I opened the bottle again and water denver poured out through the straw due to the difference in pressure between the air trapped in the bottle and the thin Denver air. Figure 2 shows the bottle's configuration when I opened it. You could approximate this as flow through a pipe size reduction, as shown in Figure 3. LA A. Calculate the instantaneous flow rate at the moment I opened the bottle in Denver. The straw has an inside diameter of 1/2 cm. Provide your answer in cubic cm per second to three decimal places. State all assumptions. • If you treat the air pressure in Denver as 0, then the pressure in the bottle, for the purposes of this problem, would be the difference in pressure between LA and Denver B. How much water spills before the pressure in the bottle equalizes with the air pressure in Denver? Provide your answer in milliliters to three decimal places. State all assumptions. • Use the ideal gas law, PV = nRT, to find the volume of air in the bottle. The mass of gas inside the bottle and the temperature remains constant. That means nRT doesn't change, so PLAVLA = PDennerV Denner. NOTE: you don't need to know n or R! Don't waste your time. De H₂ I H₂

I took a flight from Los Angeles to Denver, and I carried with me a closed water bottle of the type that delivers water to me through a built-in straw (see Figure 1). The bottle has an internal diameter of D = 6 cm, and an internal height of H₂ = 25cm. It is A% filled with water. The straw tip (outlet)H = H₂ + 3cm. The last time I opened the bottle before I departed was at LAX, where the atmospheric pressure wasP = B hPa. While waiting for my ride at Denver International Airport, atmospheric pressure? = C hPa, I opened the bottle again and water denver poured out through the straw due to the difference in pressure between the air trapped in the bottle and the thin Denver air. Figure 2 shows the bottle's configuration when I opened it. You could approximate this as flow through a pipe size reduction, as shown in Figure 3. LA A. Calculate the instantaneous flow rate at the moment I opened the bottle in Denver. The straw has an inside diameter of 1/2 cm. Provide your answer in cubic cm per second to three decimal places. State all assumptions. • If you treat the air pressure in Denver as 0, then the pressure in the bottle, for the purposes of this problem, would be the difference in pressure between LA and Denver B. How much water spills before the pressure in the bottle equalizes with the air pressure in Denver? Provide your answer in milliliters to three decimal places. State all assumptions. • Use the ideal gas law, PV = nRT, to find the volume of air in the bottle. The mass of gas inside the bottle and the temperature remains constant. That means nRT doesn't change, so PLAVLA = PDennerV Denner. NOTE: you don't need to know n or R! Don't waste your time. De H₂ I H₂

Elements Of Electromagnetics
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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100%

Please show all your work neatly including finding the correct units.

for : A% = 40+51, so A =91%

for : P_LA=B hPa. B= 0+1012, so B = 1012

for : P_denver=C hPa. C=3+838, so C =841

 

### Educational Exercise: Water Bottle Pressure Dynamics **Problem Statement:** I took a flight from Los Angeles to Denver, and I carried with me a closed water bottle of the type that delivers water to me through a built-in straw (see Figure 1). The bottle has an internal diameter of \(D = 6 \text{ cm}\), and an internal height of \(H_B = 25 \text{cm}\). It is \(A\%\) filled with water. The straw tip (outlet) \(H_s = H_B + 3 \text{cm}\). The last time I opened the bottle before I departed was at LAX, where the atmospheric pressure was \(P_{LA} = B \text{ hPa}\). **Scenario:** While waiting for my ride at Denver International Airport, atmospheric pressure \(P_{Denver} = C \text{ hPa}\), I opened the bottle again and water poured out through the straw due to the difference in pressure between the air trapped in the bottle and the thin Denver air. Figure 2 shows the bottle’s configuration when I opened it. You could approximate this as flow through a pipe size reduction, as shown in Figure 3. **Tasks:** **A. Calculate the instantaneous flow rate at the moment I opened the bottle in Denver.** - The straw has an inside diameter of \(1/2 \text{ cm}\). Provide your answer in cubic cm per second to three decimal places. State all assumptions. - Hint: - If you treat the air pressure in Denver as 0, then the pressure in the bottle, for the purposes of this problem, would be the difference in pressure between LA and Denver. **B. How much water spills before the pressure in the bottle equalizes with the air pressure in Denver?** - Provide your answer in milliliters to three decimal places. State all assumptions. - Use the ideal gas law, \(PV = nRT\), to find the volume of air in the bottle. The mass of gas inside the bottle and the temperature remains constant. That means \(nRT\) doesn't change, so: \[ P_{LA} V_{LA} = P_{Denver} V_{Denver} \] **Important Note:** - You don’t need to know \(n\) or \(R\)! Don’t waste your time. #### Figures: **Figure 1: [Water Bottle Structure]**
Transcribed Image Text:### Educational Exercise: Water Bottle Pressure Dynamics **Problem Statement:** I took a flight from Los Angeles to Denver, and I carried with me a closed water bottle of the type that delivers water to me through a built-in straw (see Figure 1). The bottle has an internal diameter of \(D = 6 \text{ cm}\), and an internal height of \(H_B = 25 \text{cm}\). It is \(A\%\) filled with water. The straw tip (outlet) \(H_s = H_B + 3 \text{cm}\). The last time I opened the bottle before I departed was at LAX, where the atmospheric pressure was \(P_{LA} = B \text{ hPa}\). **Scenario:** While waiting for my ride at Denver International Airport, atmospheric pressure \(P_{Denver} = C \text{ hPa}\), I opened the bottle again and water poured out through the straw due to the difference in pressure between the air trapped in the bottle and the thin Denver air. Figure 2 shows the bottle’s configuration when I opened it. You could approximate this as flow through a pipe size reduction, as shown in Figure 3. **Tasks:** **A. Calculate the instantaneous flow rate at the moment I opened the bottle in Denver.** - The straw has an inside diameter of \(1/2 \text{ cm}\). Provide your answer in cubic cm per second to three decimal places. State all assumptions. - Hint: - If you treat the air pressure in Denver as 0, then the pressure in the bottle, for the purposes of this problem, would be the difference in pressure between LA and Denver. **B. How much water spills before the pressure in the bottle equalizes with the air pressure in Denver?** - Provide your answer in milliliters to three decimal places. State all assumptions. - Use the ideal gas law, \(PV = nRT\), to find the volume of air in the bottle. The mass of gas inside the bottle and the temperature remains constant. That means \(nRT\) doesn't change, so: \[ P_{LA} V_{LA} = P_{Denver} V_{Denver} \] **Important Note:** - You don’t need to know \(n\) or \(R\)! Don’t waste your time. #### Figures: **Figure 1: [Water Bottle Structure]**
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