What is Upthrust?
All liquids acquire force on the immersing or submerging bodies on it. This goes slightly against the gravity. Tise pushing force of the liquid increases even vigorously on going deeper down and generates a pressure on the object with net upward force. This upward force exerted by fluid molecules is known as the upthrust. Thus, the liquid applies force from all possible directions to pressurize the object.ย
Upthrust lifts the object upward and shows the sinking or floating actions. These sinks and floats also have their own mechanism. Let’s dive into the liquid theoretically to get more knowledge about its behavior.
Archimedes’ Principle: Why Objects Float or Sink
Archimedesโ principle highlights that every full or half submerged object feels an upward force, known as upthrust, in the liquid. This mathematical force will be equal to the weight of the fluid driven out by that object. The Greek mathematician Archimedes established this theory behind floating and sinking, about 2,000 years ago, leaving its superiority in fluid mechanics.
A body with greater density, overcoming the density of fluid, gets lost inside the liquid reaching the surface. Conversely, if the fluidโs density is greater, the object keeps drifting on it. Again on the equality of both densities, the object remains submerged in the fluid. The concept simply stands in the rivalry of buoyancy and gravity. The heroic implication of this easy concept can be seen in the floating ship. The metallic ship with hollow inside is designed for displacing larger volume of water, which makes it float, even though composed of a substance denser than water. Other surprisingly interesting facts also lie beneath the Archimedes principle.
Some mythical statements tell that Archimedes got this idea while taking a bath. He saw how the water rose as he went in the tub. The beauty of discovering hidden treasures of the natural principles by daily circumstances’ observation is captured by his delighted revelation. “Eureka!” was popped out from his mouth by identifying his joyous discovery. This spirit of interest keeps motivating huge discoveries.
Upthrust Formula and Key Variables (ฯ, V, g)
The formula for calculating upthrust or Buoyant force (FB) is given by Archimedes,
FB = โด.V.g [Equation 1]
Where:
- FB = Upthrust (in newtons)
- โด = Density of the fluid
- V = Volume of fluid displaced
- g = Acceleration due to gravity
The above equation calculates the amount of upward push a fluid provides to an object immersed in it. The upthrust pulls the object upward that increases with the fluid’s density and volume displacement.
Factors Affecting Upthrust
Upthrust is also affected by sudden variable quantities which are given below:
- Density of the Fluid (โด): A higher density fluid generates higher upthrust with the same displaced volume of fluid.
- Volume of Displaced Fluid (V): Greater volume displaced means greater upthrust.
- Gravitational Acceleration (g): Upthrust as seen in equation [1] is directly proportional to the acceleration due to gravity. However, it may remain constant at earth, upthrust behaves according to โgโ in some other regions.
- Shape and Orientation of the Object: Extra upthrust is experienced by structures that expel more fluid, such as boats with a flat bottom.
- Immersion Depth: An object keeps on displacing more fluid the deeper it submerges, until it gets entirely submerged.
- Fluid Density
As per equation[1], density has a direct relation with upthrust. Thus, a dense liquid glycerin shows greater upthrust than in less dense water.
- Displaced Volume
An object drives that extent of fluid volume which is equal to the volume of its submerged portion. Thus, a dense object can also experience greater upthrust if it displaces more volume of the fluid.
Difference Between Upthrust, Weight, and Apparent Weight
Weight, apparent weight and upthrust are three confusing matters in fluid mechanics. Therefore a clear explanation is required. They are characterized below:
- Weight is the force of a massive object with which it makes an object fall towards it. The term arises along with the gravitational force and the gravitational acceleration of the falling object. All objects of a certain mass experience weight in the presence of gravity. It is a downward force. (Weight = mass ร acceleration due to gravity)
- Upthrust pushes or pulls an object depending upon the fluidโs and the objectโs density. It generally is called upward force due to the push it exerts on less or equally dense objects. ( Upthrust = โด.V.g)
- Apparent Weight arises due to the upthrust. Due to the reduction of gravity by the action of fluidโs force the weight is also reduced while being inside the fluid which is called the apparent weight.
(Apparent weight = Actual weight – Buoyant force)
For example, stone lifted inside a river feels lighter when it is inside water but becomes heavier as soon as it comes out of water.
Measuring Upthrust with Spring Balances and Hydrometers
Both of these devices do not give a direct measurement, but the upthrust is deduced from their weight and density measurements,
- Spring Balances: To measure the upthrust, an object is weighed first in air using the spring balance and then in water. Hence, the difference is calculated.
- Hydrometers: Hydrometers measure the density of fluids. Because of a greater upthrust in dense fluids, it floats upward. This floating extent can help in measuring the upthrust.
Real-World Examples of Upthrust in Action
- Floating of ice in water
Ice is of less density than water and hence floats in water. - Swimming and floating bodies
Human bodies displace water and experience an upward force on water. As saline water has a higher fluid density and more upthrust, people float better on seas and oceans. - Ships: Ships are intentionally designed structures to create enough upthrust by displacing a significant amount of water. Although being built out of metal, ships’ internal hollow design increases the quantity of displacement.
Upthrust vs. Buoyancy: Are They the Same?
“Upthrust” and “Buoyancy” may look quite similar and be spoken interchangeably. However, they are a bit different.
- Upthrust is that push of the fluid which generates force and makes low or equally dense objects keep floating or remain submerged in it. It is the cause for buoyancy.
- Buoyancy appears as a result of upthrust which is just a term used to denote the floating or submerging property.
Applications of Upthrust in Engineering and Daily Life
Many structures are designed and applied in engineering and also in daily life that directly relate to upthrust. Some examples are given below:
- Floating structures: Not only ships that float on water but also ships floating on air called airships rely on Archimedes principle of upthrust. Some floating homes are also designed in the Netherlands with required hollow space in the base to prevent from sinking.
- Hydraulics and Fluid Mechanics: Fluid pressure and buoyancy concepts are used in devices like hydraulic lifts.
- Water Sports: In rafting or just a boat trip, life jackets are essentially used to increase the volume of displaced fluid without much mass. A non-swimmer can also enjoy swimming with the use of pool-float which enhances upthrust and keeps people afloat.
- Oil Industry: Upthrust is used by equipment in specific industrial processes to distinguish fluids with various densities (such as water and oil) for reprocessing and filtration.
- Weather Balloons: They are used for atmospheric research since they rise due to the upthrust generated by lighter-than-air gases like helium.
Common Misconceptions About Upthrust Explained
- Heavier objects always sink.
Rather than weight, the action of floating or sinking is decided by the relative densities of the fluid and the object placed over it. If a heavy object releases fluid identical to its weight, it can also float the same way. Also, we have to remember that upthrust doesnโt exist in vacuum as a vacuum is a fluid free region.
- Buoyancy and Upthrust are the same
They may be mistaken for the same terms. We have to keep in mind that, upthrust the upward force causes the floating action which is termed as buoyancy.
- Buoyancy only occurs in liquids.
Buoyancy is the case study in fluid dynamics and gases and liquids both are fluids. Hot air balloons exist due to the finest action of gaseous buoyancy.
- Upthrust increases with depth.
After complete submersion, upthrust for incompressible fluids like water is determined by volume displaced rather than depth.
Practice Problems: Calculating Upthrust Step by Step
Qns no. 1: A wooden block having volume 0.003 m^3 is completely submerged in water. Calculate the upthrust.
Solution:
Given,
Volume (V) = 0.003 m^3
Density (โด) = 1000 kg/m^3
g = 9.8 m/s^2
Using equation [1] we have, FB = 1000 ร 0.002 ร 9.8 = 29.4 N
Qns no. 2: An object weighing 60 N in air has 40 N weights while submerged in water. What will be the upthrust?
Solution:
Given,
Actual weight of iron= 60 N
Apparent weight of iron in water= 40 N
Now, Upthrust = 60 – 40 = 20 N
Therefore, the upthrust will be 20 N.
Qns no. 3: An object weighing 100 N in air is submerged in water and displaces 0.005 mยณ of water. What is its apparent weight?
Solution:
Given,
Weight of iron (Actual weight) = 100 N
Volume of water (V) = 0.005 m^3
We know, density of water(โด) = 1000 kg/m^3
g = 9.8 m/s^2
From [1], upthrust = 1000 ร 0.005 ร 9.8 = 49 N
Again, Apparent weight = Actual weight – Upthrust = 100 – 49 = 51 N
Therefore, we got the apparent weight as 51 N.
Conclusion
The logic behind why objects hover or sink in fluids is explained by the simplest concept of upthrust in physics and fluid dynamics. Archimedes’ Principle covers a huge range from the floating of humans in water to floating of ships. Superior designs can be prepared by the proper choice of objects with required elements that affect upthrust. By clearing up frequent confusions and building strong mathematics, students can grasp this small but mighty force influencing our environment.
References
Lindsay, F. J. M. (1970). Archimedian upthrust.ย Physics Education,ย 5(6), 370.
https://www.geeksforgeeks.org/physics/difference-between-buoyancy-and-upthrust/
https://keystagewiki.com/index.php/Upthrust
https://gimnazijapg.me/images/pdfdoc/fizika/II_razred/buoyant-force-and-archimedes-principle.pdf
https://www.scipitutor.com/physics/upthrust
