### Hydrostatic Pressure and Manometry Problem#### IntroductionA gate of length \( l \) and width \( b \) is submerged in water, which has a density \( \rho_w \), as depicted in the figure below. Hydrostatic pressure acts on the gate on one side and the other side contains pressurized air that is pressurized to \( P_2 \) such that the gate is at equilibrium with the net pressure forces on both sides. Attached to this chamber is a manometer filled with mercury of density \( \rho_{Hg} \). #### Problem StatementFind the height of the mercury column \( \Delta h \) in terms of the following values as needed: \[ P_{atm}, \rho_w, \rho_{Hg}, g, \theta, \text{and} \ l. \]You may neglect pressure variations due to height differences in the air but not either of the liquids. You may also neglect the weight of the gate. Make sure to draw a free body diagram.#### Diagram DescriptionThe diagram illustrates the setup as follows:- The water (with density \( \rho_w \)) on the left side of the gate.- The gate of length \( l \) and width \( b \) positioned at an angle \( \theta \) to the horizontal.- Point \( A \) at the point of contact between the gate and the water surface.- \( P_{atm} \) is the atmospheric pressure acting on the surface of the water.- \( P_2 \) is the pressure of the air on the right side of the gate.- A manometer containing mercury is connected to the air chamber to measure the pressure difference.- The mercury column has a height difference \( \Delta h \) which is used to determine the pressure \( P_2 \). One side (the left side) of the manometer is open to the atmosphere, while the other side is connected to the air chamber. The height difference \( \Delta h \) in the mercury levels indicates the pressure difference between the chamber and the atmosphere.### Explanation of Equilibrium:Assuming equilibrium, the hydrostatic pressure force on the gate due to the water must be balanced by the pressure force due to the air on the other side of the gate. The hydrostatic pressure formula and the pressure difference indicated by the mercury column will be used to derive the required height \( \Delta h \).#### Free Body Diagram

Name: ### Hydrostatic Pressure and Manometry Problem#### IntroductionA gate
Uploaded: 2024-03-20T06:56:55.000Z
Channel: Bartleby
Description: ### Hydrostatic Pressure and Manometry Problem#### IntroductionA gate of length \( l \) and width \( b \) is submerged in water, which has a density \( \rho_w \), as depicted in the figure below. Hydrostatic pressure acts on the gate on one side and

Answered: Image /qna-images/answer/2edfd167-180c-4394-8c46-b5b333995d2d.jpg

Engineering

Mechanical Engineering

A gate of length l and width b is submerged in water, which has density Pw, as depicted in the figure below. Hydrostatic pressure acts on the gate on one side and the other side contains pressurized air that is pressurized to P2 such that the gate is at equilibrium with the net pressure forces on both sides. Attached to this chamber is a manometer filled with mercury of density PHg. Find the height of the mercury column Ah in terms of the following values as needed: Patm, Pw. PHg, 9, 0, and l. You may neglect pressure variations due to height differences in the air but not either of the liquids. You may also neglect the weight of the gate. Make sure to draw a free body diagram. Patm Pw P2 Ah PHg

A gate of length l and width b is submerged in water, which has density Pw, as depicted in the figure below. Hydrostatic pressure acts on the gate on one side and the other side contains pressurized air that is pressurized to P2 such that the gate is at equilibrium with the net pressure forces on both sides. Attached to this chamber is a manometer filled with mercury of density PHg. Find the height of the mercury column Ah in terms of the following values as needed: Patm, Pw. PHg, 9, 0, and l. You may neglect pressure variations due to height differences in the air but not either of the liquids. You may also neglect the weight of the gate. Make sure to draw a free body diagram. Patm Pw P2 Ah PHg

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

See similar textbooks

Similar questions

Please show ALL calculations step by step
The shown figure represents a tank filled with water and closed at its top with gate AB and connected with a manometer at its bottom. The gate can be rotated about the hinge at A. Compute the minimum height (y). of mercury_(Hg) in the manometer that is required to cause the gate just starts to open. Assume: Specific gravity of Hg=13.6, Mass density of the gate= 2500 kg/m3. Material of the gate is homogenous. Gate width is 1.0 m, and gate thickness is 2.0 cm. Hinge. LA 1000 N.m r=0.5m water B y Hg 0.25m 0.25m, 0.5m
Solve correctly please, with detailed explanation required.
The gauge pressure in the air container illustrated in the figure is 80 kPa. Calculate the differential height h of the mercury column. Consider the atmospheric pressure to be zero.
Smwidth x Sm leng th The plate used to support the water as shown in Figure Q1 (c) is a S sn square. The value of h is 4.5 m. Ignore the atmospheric pressure, determine the tension of the горе, Т. (c) T Rope h 450 Figure QI (c)
A 1.0m diameter tank having equal layers of water, oil(SG=0.80), and another liquid with SG=1.62, with each layer is 0.65 m in height is being observed. Find the gauge pressure (kPa) in between the layers of water and oil.
3.) The system in the figure below is at 20 °C. If the pressure at point A is 2900 lb/ft2, determine the pressures at points B, C, and D. Air Air 3ft 4ft Air 5ft 6t Water 2 ft
In the system in the figure, the atmospheric pressure is 101325 Pa and the tank If the pressure at the bottom is 275000 Pa, the density of the fluid find?
Consider the pressure and force acting on the pool retaining a reservoir of water. Suppose the pool is 50m wide and the water is 8m deep, as illustrated below. (a) What is the Gauge pressure on the dam due to the water? (b) What is the absolute pressure at10m depth of the dam? (C) Calculate the force exerted against the dam. Density of water is 1000kg/m3.
Need solution ASAP
Both a and b otherwise skip please i will upvote for sure
The U tube differential manometer is connected between two pipes, with the specific gravity of liquid in pipe A & in pipe B is 0.84 and 0.63 respectively as shown in the figure, h;= 104 cm, hz = 28 cm, mercury level difference hg = 16 cm. Find the difference in pressure between the pipes A & B in kPa. (ENTER ONLY THE VALUE IN THE BOXES BY REFERRING THE UNIT GIVEN IN BRACKET. ALSO UPLOAD YOUR HAND WRITTEN ANSWERS IN THE LINK PROVIDED) h2 hi hg The difference in pressure between pipes A &B (in kPa)