**Understanding Hydrometer Measurements and the Float Level**A hydrometer is an instrument used to measure the specific gravity (SG) of a liquid, which is the ratio of the density of the liquid to the density of water. The hydrometer consists of a calibrated stem and a weighted bulb that allows it to float. **Problem Statement:**Given:- The float level \( h \) of the hydrometer is a measure of the specific gravity of the liquid.- For stem diameter \( D \) and total weight \( W \),- If \( h = 0 \) represents SG = 1.0,**Question:**What is the formula for \( h \) as a function of \( W, D, \) SG, and \( \gamma_0 \) for water?**Diagram Explanation:**The diagram provided showcases a hydrometer floating in a liquid of specific gravity greater than 1 (SG > 1). - The vertical component \( h \) is the floating height measured from the fluid's surface to a marked point on the stem.- The diameter of the stem where the measurement takes place is \( D \).- The label SG = 1.0 corresponds to the point where \( h = 0 \).- The total weight of the hydrometer is \( W \).- The fluid in which the hydrometer is immersed has a specific gravity greater than one compared to water.**Visual Guide:**- The hydrometer is partially submerged, with its weighted bulb below and the stem extending upwards.- The diagram indicates fluid with specific gravity greater than one around the hydrometer's bulb.- The stem diameter \( D \) is clearly marked near the top of the fluid level.This setup helps learners understand how changes in specific gravity of the fluid affect the float level \( h \) of the hydrometer. The relationship between the hydrometer’s weight, the diameter of its stem, and the specific gravity of the fluid are crucial in determining the formula for \( h \). ### Multiple Choice Questions#### Question:Calculate the value of \( h \) using the correct formula. Please select the correct formula for \( h \) from the options below:1. \[ h = \frac{W(SG - 1)}{SG \gamma_0 \left(\frac{\pi}{4}D^2 \right)} \]2. \[ h = \frac{(SG + 1)}{W \cdot SG \gamma_0 \left(\frac{\pi}{4}D^2 \right)} \]3. \[ h = \frac{W \left(\frac{\pi}{4} D^2 \right)}{(SG - 1) \gamma_0} \]4. \[ h = \frac{W \left(\frac{\pi}{4} D^2 \right)}{(SG + 1) \gamma_0} \]### Explanation of Diagram:The image contains four options for calculating the value of \( h \). Each option includes a formula that involves the following variables:- \( W \) : Weight- \( SG \) : Specific Gravity- \( \gamma_0 \) : Unit Weight of Water- \( D \) : Diameter- \(\pi\) : Pi (approximately 3.14159)Each formula uses these variables with different operations and combinations to solve for \( h \). Please carefully review the options and choose the one that correctly calculates the value of \( h \).

Answered: Image /qna-images/answer/d9484e50-9e8d-43c2-be34-db6e05bcc9f5.jpg

The float level h of a hydrometer is a measure of the specific gravity of the liquid. For stem diameter D and total weight W, if h= 0 represents SG=1.0, what is the formula for has a function of W, D, SG, and yo for water? D SG=1.0 Fluid, SG > 1

The float level h of a hydrometer is a measure of the specific gravity of the liquid. For stem diameter D and total weight W, if h= 0 represents SG=1.0, what is the formula for has a function of W, D, SG, and yo for water? D SG=1.0 Fluid, SG > 1

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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