How long will it take the water surface in the tank shown to  drop from h = 3 m to h = 50 cm?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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How long will it take the water surface in the tank shown to 
drop from h = 3 m to h = 50 cm? 

**Problem 5.75: Valve Flow and Pressure Drop**

The diagram illustrates a valve setup with the following components:
- A stem connected to a disk, enclosed by a bonnet.
- Packing material to ensure a tight seal.
- A body that houses the valve's internal elements.
- A seat against which the disk seals.
- An opening for fluid flow.

The problem involves estimating the pressure drop across the valve using the Bernoulli equation, given a 10-gpm flow of water at 60°F. The upstream pipe has an inside diameter of 1 inch. The distance across the seat is 1/8 inch, with the valve opening at 1/2 inch in diameter. 

**Problem 5.76: Flow Through an Orifice**

An orifice flow situation involves a minimum area, "vena contracta," where the area ratio to the orifice is 0.64.

Tasks:
a. Derive a discharge equation using \( Q = C_d A_o (2 \Delta p / \rho)^{1/2} \), where \( A_o \) is the orifice area, and \( \Delta p \) is the pressure difference.

Note: "psid" indicates differential pressure, not absolute or gauge.

**Problem 5.78: Oxygen Leak**

Oxygen leaks from a small orifice in a bottle. The scenario includes:
- Bottle volume: 0.1 m³
- Orifice diameter: 0.12 mm
- Temperature: 18°C
- Mass-flow rate: \( \dot{m} = 0.68 \, \text{Pa} / \sqrt{RT} \)

Objective: Determine the time for pressure to drop from 10 to 5 MPa.

**Problem 5.79: Water Surface Drop in Tank**

A tank of 60 cm diameter and liquid height \( h \) is connected to a 3 cm diameter pipe. The equation for flow is \( V = \sqrt{2gh} \).

Objective: Calculate the duration for water surface level to drop from 3 m to 50 cm.

**Problem 5.80: Pressurized Tank Drainage**

For a draining pressurized tank:
- The exit velocity \( V_e \) is calculated as \( V_e = \sqrt{ \frac{2p}{\rho} + 2gh} \).

These problems explore fluid mechanics concepts involving flow dynamics through valves,
Transcribed Image Text:**Problem 5.75: Valve Flow and Pressure Drop** The diagram illustrates a valve setup with the following components: - A stem connected to a disk, enclosed by a bonnet. - Packing material to ensure a tight seal. - A body that houses the valve's internal elements. - A seat against which the disk seals. - An opening for fluid flow. The problem involves estimating the pressure drop across the valve using the Bernoulli equation, given a 10-gpm flow of water at 60°F. The upstream pipe has an inside diameter of 1 inch. The distance across the seat is 1/8 inch, with the valve opening at 1/2 inch in diameter. **Problem 5.76: Flow Through an Orifice** An orifice flow situation involves a minimum area, "vena contracta," where the area ratio to the orifice is 0.64. Tasks: a. Derive a discharge equation using \( Q = C_d A_o (2 \Delta p / \rho)^{1/2} \), where \( A_o \) is the orifice area, and \( \Delta p \) is the pressure difference. Note: "psid" indicates differential pressure, not absolute or gauge. **Problem 5.78: Oxygen Leak** Oxygen leaks from a small orifice in a bottle. The scenario includes: - Bottle volume: 0.1 m³ - Orifice diameter: 0.12 mm - Temperature: 18°C - Mass-flow rate: \( \dot{m} = 0.68 \, \text{Pa} / \sqrt{RT} \) Objective: Determine the time for pressure to drop from 10 to 5 MPa. **Problem 5.79: Water Surface Drop in Tank** A tank of 60 cm diameter and liquid height \( h \) is connected to a 3 cm diameter pipe. The equation for flow is \( V = \sqrt{2gh} \). Objective: Calculate the duration for water surface level to drop from 3 m to 50 cm. **Problem 5.80: Pressurized Tank Drainage** For a draining pressurized tank: - The exit velocity \( V_e \) is calculated as \( V_e = \sqrt{ \frac{2p}{\rho} + 2gh} \). These problems explore fluid mechanics concepts involving flow dynamics through valves,
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