Welcome to The Buoyancy Force Lab II!
Richard Williams
Principal of Phaethon Research for Clean Energy and Arethusa Investing In Clean Water
Introduction
In Parts 1 and 2, there are examples of how changes in the buoyancy of bubbles and balloons put the bottom of the sea and upper reaches of the atmosphere within human grasp! Now it is time to present Buoyancy Force as a tool for visualization . The characterization of Buoyancy as a force means it is governed by Newtons three laws of motion.
Our focus here is on laws 2 and 3. The second law equates force with the mass of the body in motion times its acceleration. Acceleration is the change in velocity divided by the change in time. Thus we need to identify what is the mass and what is the acceleration!
The third law states that for every force there is an opposite and equal opposing force. Therefore, when we wish to find magnitude of the buoyancy force, we first start by calculating its equal opposing force, gravity. How to visualize three Buoyancy Force Situations: Neutral Buoyancy; Positive Buoyancy and Negative Buoyancy Lets return to the cover photo and focus on what happens when the boat enters the water.
Phaethon Research and https://www.boydcorp.com/blog/buoyancy-drives-natural-convection.html
Splash is the mass of water that jumps out of the sea when the boat enters the water. The mass of Splash is the same as the boat that is immersed in water, but not the mast and sail and portion of the boat above the surface. After the boat stabilizes in the water, neither rising nor falling, it is at neutral buoyancy! The black area under boat is where water comes from! As soon as Splash is displaced out of the water, the black area is a vacuum. The water highlighted in orange below is from the bottom and each side of the vacuum. It immediately rushes in to fill the space.
Phaethon Research and https://www.boydcorp.com/blog/buoyancy-drives-natural-convection.html
This elimination of the vacuum explains how the Bubble Plume technique uses bubbles to mix the three thermally distinct layers of water in a lake or reservoir.
https://www.unsw.edu.au/research/wrl/our-research/cold-water-pollution-a-review This was discussed in Look at What You Can Do with Bubbles!https://www.dhirubhai.net/in/richard-williams-68268b24/
Returning to our initial example, suppose the boat holds a huge crate of bananas at the time it enters the water. When the boat sails to the green mountain and unloads the bananas, the boat will become lighter and rise up in the water. This rise causes the boat to move from neutral buoyancy to positive buoyancy.
Phaethon Research and https://www.boydcorp.com/blog/buoyancy-drives-natural-convection.html
After the bananas are unloaded, barbells are placed in the crate. Then the crate is put on the ship. The barbells are much heavier than the bananas and cause a small Splash. The displacement puts boat in a state of negative buoyancy until it begins riding lower in the water.
Phaethon Research and https://www.boydcorp.com/blog/buoyancy-drives-natural-convection.html
These three situations are the only possibilities for buoyancy at any instant in time! To begin to solve for the amount of water displaced or the maximum amount of barbells the boat can carry before sinking, we need to imagine a relationship between the boat and the sea.! The Formula for Calculating Buoyancy and numerical example Archimedes of Syracuse, one of the smartest who ever lived states the relationship in just 4 variables.
Fb = Volume of object displaced x density of fluid containing object displaced x gravity
Google AI Overview
Firs, let's understand the buoyant force as something capable of moving an object at rest to motion or as imbalance of forces causing a change in objects speed and direction. This is Newton's First Law of Motion. All formulas for force reduce to mass times change in velocity also known as acceleration. Lets apply this formula to our boat example.
This formula measures the force water exerts on the boat, Fb, to push it higher in the water. The variable p is the density of the water. If the water is more dense, the water is heavier and harder to displace. The variable g is the weak force of attraction between all objects that have mass that is called gravity. (while gravity is treated as a constant for most situations at or near the earth's surface, it decreases as you move high in the atmosphere and to outer space. It increases if you are deep in the Earth's crust or mantle. ) The final variable,v ,fluid volume contains the mass displaced. Multiplying v x p results in numerical value of the mass.
For readers who benefit from seeing calculations, I present the following example posted by Submitted by Ashley A.
8. Calculate the buoyancy force for a ship, using: Fb = how (volume) g g = gravity = 9.8 m/s2 volume of displacement = 5000 m3 how = density of sea water = 1025 kg/m3
Submitted by Ashley A. Sep. 02, 2023 11:05 p.m.
ANSWER
Fb = 1025 kg/m3 x 5000 m3 x 9.8 meters /sec2 =50,225,000 Newtons( units of newton = kilogram meters/Sec2)
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The components of the Buoyancy Force: p, g and volume change with altitude, depth, temperature, and pressure. The diagram below depicts a blimp with a flexible frame, filled with helium rising through a thermally stratified lake or reservoir. Observe changes at three levels in the water and the fourth in the air! The season is summer and time of day is afternoon. Sun will be a factor during the ascent of the balloon from the lake or reservoir into the air because it will heat the helium and increase pressure inside the blimp.
By Mbrookings19 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=69783069!Phaethon Research and https://en.wikipedia.org/wiki/Lake_stratification
In addition to temperature, density, and pressure changing, the fluid through which the blimp ascends becomes air instead of water.
Helium at atmospheric temperature and pressure is pumped into the blimp at the surface and then brought to bottom of the reservoir. The high pressure compresses the balloon according to the Ideal Gas Law, PV = nRT. where P = Pressure V= Volume N= Number of moles of a gas R= Gas Constant for Helium T= Temperature in degrees Kelvin. At the bottom ,the temperature inside the balloon is not significantly higher than the surface temperature because the pressure. increase is matched by proportionate reduction in the volume according to Boyles's Law and the Ideal Gas Law.
An example of this phenomenon was illustrated in storage of compressed air in Look At What You Can Do With Balloons!https://www.dhirubhai.net/in/richard-williams-68268b24/
//www.nytimes.com/2024/03/18/science/renewable-energy-storage-climate.html#:~:text=Energy%20Dome%20uses%20carbon%20dioxide,the%20carbon%20dioxide%20into%20liquid
Given water has a great capacity to accept heat, heat is leaving the balloon quickly at the lowest depth where the temperature is cold! As the balloon ascends, pressure inside the balloon drops. The temperature also drops and slows the loss of the heat to water. In both water and, resistance to balloon's motion, known as drag will reduce balloon velocity!
The rate of heat loss is also affected by material the balloon is made of. The balloon material may also affect the absorption of solar infrared radiation. (infrared causes heat) Movement to air from water, immediately reduces the outflow of heat because air is not nearly as good at accepting heat. It also exposes the balloon to elements of weather such as waves, sunshine, wind, rain, snow, thunder and lightning.
Effects of Weather upon Density, Pressure and Volume of The Balloon
The density of the helium in the balloon relative to the density of the lake or reservoir and air will dictate whether the balloon rises or falls. The elements of weather have a direct impact by either increasing or decreasing the temperature, pressure and volume. Sunshine will warm the helium. Wind or waves can either warm or cool the helium in the balloon as it facilitates the transfer of heat. Snow or rain will cause heat to leave the balloon. Thunder and lightning can cause puncture of the membrane of the balloon.
Movement of A Buoyant Object in Water And Air
Recall the diagram of the ascending blimp; set forth below are characteristics of the blimps motion that are of interest.
1 Velocity of the Blimp at time T
2. Temperature inside Blimp a time T
3. Density of the Blimp at time T
4. Heat transfer to or from bubble at time T
5. Volume of the Bubble at time T
6 Drag force at time T
7.Buoyant force at Time T
8. Heat transfer rate at time T
9, Distance Traveled from To.
These factors will be also of interest to operators of a balloon rising high in the atmosphere.
https://spaceref.com/space-commerce/stratoflight-and-expleo-join-forces-to-take-passengers-into-near-space-by-balloon/ Look At What You Can Do With Balloons!https://www.dhirubhai.net/in/richard-williams-68268b24/
For the operators of the sightseeing balloon to take passengers into near space by balloon, Calculation 7, Buoyant force at Time T, is vital! They need to know the time and the altitude where the weight of air displaced = weight of the balloon and helium. This altitude is 20 miles. google AI overview.
There are equations to calculate each of these characteristics. However these equations must be solved simultaneously. It is likely that one would use the Taylor Series Polynomial approximations or an algorithm to calculate a matrix of equations to find values for the above equations. An example of a calculation of this type would be appropriate only for limited number of readers and thus is not included in this article. Instead the example will be the subject of a future post, Into the Abyss of Calculations.
CONCLUSION
Buoyancy Force Lab encompasses a discussion of the identification of mass displaced in a fluid as Splash. The displacement of Splash creates immediate vacuum. The vacuum is filled by surrounding water, including water from the depths. This movement illustrates the mechanics of bubble plume destratification.
The Lab further relates Splash to the displacing objects volume, the fluids density, volume, temperature, pressure, mass. The fluid inside a balloon or bubble is gas. This brings The Ideal Gas law into play! The storage of gas under high pressure at the bottom of a lake exemplifies this phenomenon. Like The Ideal Gas Law, heat transfer is an ever-present companion of buoyancy.
Heat transfer dictates the relative density of the air filled object to the external fluid. Waves and elements of weather as well the material that contains air will affect the heat transferred.
Newton's second law defines Buoyancy as equal to an opposing force. Solving for gravitational force is a step to solving for characteristics of Buoyancy the opposing force. Of particular interest is a rising balloon or bubble is the time and altitude of neutral buoyancy. Grasping these ideas accomplishes the goal of this lab, but avoids leaping in the abyss of complex calculations.