**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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Unit Conversion

Standard units are also called SI units. SI units are used for measuring a physical quantity satisfying certain conditions. There are two types of units: fundamental units and derived units. Fundamental units are physical quantities that are independent, that is, they do not depend on other quantities like mass, length, or time. There are plenty of quantities in our lives which need to be measured and compared. Measuring is the comparison of a particular physical quantity with its reference value. A unit is a measure of a fixed physical quantity. A physical quantity is the product of a unit and the numerical value we need to compare with.

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**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 \( h \).

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