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Force given Surface Tension using Wilhelmy-Plate Method Calculator

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✖The Density of Plate is the ratio of the mass of the plate to its volume.ⓘ Density of Plate [ρp]
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-10%
✖Length of Plate is the distance between two extreme points along one side of the base plate.ⓘ Length of Plate [L]
+10%
-10%
✖Width of Full Size Bearing Plate is the smaller dimension of plate.ⓘ Width of Full Size Bearing Plate [B]
+10%
-10%
✖Thickness of Plate is defined as the thickness of plate (usually the lowest dimension of the plate) under consideration.ⓘ Thickness of Plate [t]
+10%
-10%
✖Surface Tension of Fluid is the energy or work required to increase the surface area of a fluid due to intermolecular forces.ⓘ Surface Tension of Fluid [γ]
+10%
-10%
✖The Contact Angle is an angle that a liquid creates with a solid surface or capillary walls of a porous material when both materials come in contact together.ⓘ Contact Angle [θ]
+10%
-10%
✖Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.ⓘ Density of Fluid [ρfluid]
+10%
-10%
✖Depth of Plate is a dimension taken through the surface of the plate, usually downward from an upper surface, horizontally inward from an outer surface.ⓘ Depth of Plate [hp]
+10%
-10%
✖Force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity.ⓘ Force given Surface Tension using Wilhelmy-Plate Method [F]
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Force given Surface Tension using Wilhelmy-Plate Method

Formula
`"F" = ("ρ"_{"p"}*"[g]"*("L"*"B"*"t"))+(2*"γ"*("t"+"B")*(cos("θ")))-("ρ"_{"fluid"}*"[g]"*"t"*"B"*"h"_{"p"})`

Example
`"4.2E^9N"=("12.2kg/m³"*"[g]"*("50mm"*"200mm"*"5000mm"))+(2*"73mN/m"*("5000mm"+"200mm")*(cos("15.1°")))-("14.9kg/m³"*"[g]"*"5000mm"*"200mm"*"12.1mm")`

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Force given Surface Tension using Wilhelmy-Plate Method Solution

STEP 0: Pre-Calculation Summary
Formula Used
Force = (Density of Plate*[g]*(Length of Plate*Width of Full Size Bearing Plate*Thickness of Plate))+(2*Surface Tension of Fluid*(Thickness of Plate+Width of Full Size Bearing Plate)*(cos(Contact Angle)))-(Density of Fluid*[g]*Thickness of Plate*Width of Full Size Bearing Plate*Depth of Plate)
F = (ρp*[g]*(L*B*t))+(2*γ*(t+B)*(cos(θ)))-(ρfluid*[g]*t*B*hp)
This formula uses 1 Constants, 1 Functions, 9 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Force - (Measured in Newton) - Force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity.
Density of Plate - (Measured in Kilogram per Cubic Meter) - The Density of Plate is the ratio of the mass of the plate to its volume.
Length of Plate - (Measured in Millimeter) - Length of Plate is the distance between two extreme points along one side of the base plate.
Width of Full Size Bearing Plate - (Measured in Millimeter) - Width of Full Size Bearing Plate is the smaller dimension of plate.
Thickness of Plate - (Measured in Millimeter) - Thickness of Plate is defined as the thickness of plate (usually the lowest dimension of the plate) under consideration.
Surface Tension of Fluid - (Measured in Newton per Meter) - Surface Tension of Fluid is the energy or work required to increase the surface area of a fluid due to intermolecular forces.
Contact Angle - (Measured in Radian) - The Contact Angle is an angle that a liquid creates with a solid surface or capillary walls of a porous material when both materials come in contact together.
Density of Fluid - (Measured in Kilogram per Cubic Meter) - Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.
Depth of Plate - (Measured in Millimeter) - Depth of Plate is a dimension taken through the surface of the plate, usually downward from an upper surface, horizontally inward from an outer surface.
STEP 1: Convert Input(s) to Base Unit
Density of Plate: 12.2 Kilogram per Cubic Meter --> 12.2 Kilogram per Cubic Meter No Conversion Required
Length of Plate: 50 Millimeter --> 50 Millimeter No Conversion Required
Width of Full Size Bearing Plate: 200 Millimeter --> 200 Millimeter No Conversion Required
Thickness of Plate: 5000 Millimeter --> 5000 Millimeter No Conversion Required
Surface Tension of Fluid: 73 Millinewton per Meter --> 0.073 Newton per Meter (Check conversion here)
Contact Angle: 15.1 Degree --> 0.263544717051094 Radian (Check conversion here)
Density of Fluid: 14.9 Kilogram per Cubic Meter --> 14.9 Kilogram per Cubic Meter No Conversion Required
Depth of Plate: 12.1 Millimeter --> 12.1 Millimeter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
F = (ρp*[g]*(L*B*t))+(2*γ*(t+B)*(cos(θ)))-(ρfluid*[g]*t*B*hp) --> (12.2*[g]*(50*200*5000))+(2*0.073*(5000+200)*(cos(0.263544717051094)))-(14.9*[g]*5000*200*12.1)
Evaluating ... ...
F = 4214016304.48682
STEP 3: Convert Result to Output's Unit
4214016304.48682 Newton --> No Conversion Required
FINAL ANSWER
4214016304.48682 ≈ 4.2E+9 Newton <-- Force
(Calculation completed in 00.004 seconds)
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Home » Chemistry » Surface Chemistry » Capillarity and Surface Forces in Liquids (Curved Surfaces) » Wilhelmy-Plate Method » Force given Surface Tension using Wilhelmy-Plate Method

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Amity Institute Of Applied Sciences (AIAS, Amity University), Noida, India
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5 Wilhelmy-Plate Method Calculators

Force given Surface Tension using Wilhelmy-Plate Method
Go Force = (Density of Plate*[g]*(Length of Plate*Width of Full Size Bearing Plate*Thickness of Plate))+(2*Surface Tension of Fluid*(Thickness of Plate+Width of Full Size Bearing Plate)*(cos(Contact Angle)))-(Density of Fluid*[g]*Thickness of Plate*Width of Full Size Bearing Plate*Depth of Plate)
Force for Rectangular Plate using Wilhelmy-Plate Method
Go Force = Weight of Plate+(Surface Force*((Surface Tension of Fluid*Perimeter of Plate)-Upward Drift))
Total Weight of Plate using Wilhelmy-Plate Method
Go Total Weight of Solid Surface = Weight of Plate+Surface Tension of Fluid*(Perimeter)-Upward Drift
Total Weight of Ring using Ring-Detachment Method
Go Total Weight of Solid Surface = Weight of Ring+(4*pi*Radius of Ring*Surface Tension of Fluid)
Surface Pressure using Wilhelmy-Plate Method
Go Surface Pressure of Thin Film = -(Change in Force/(2* (Thickness of Plate+Weight of Plate)))

17 Important Formulas on Surface Tension Calculators

Force given Surface Tension using Wilhelmy-Plate Method
Go Force = (Density of Plate*[g]*(Length of Plate*Width of Full Size Bearing Plate*Thickness of Plate))+(2*Surface Tension of Fluid*(Thickness of Plate+Width of Full Size Bearing Plate)*(cos(Contact Angle)))-(Density of Fluid*[g]*Thickness of Plate*Width of Full Size Bearing Plate*Depth of Plate)
Surface Tension given Contact Angle
Go Surface Tension of Fluid = (2*Radius of Curvature*Density of Fluid*[g]*Height of Capillary Rise/Fall)*(1/cos(Contact Angle))
Surface Tension given Molecular Weight
Go Surface Tension of Fluid = [EOTVOS_C]*(Critical Temperature-Temperature-6)/(Molecular Weight/Density of Liquid)^(2/3)
Surface Tension of Pure Water
Go Surface Tension of Pure Water = 235.8*(1-(Temperature/Critical Temperature))^(1.256)*(1-(0.625*(1-(Temperature/Critical Temperature))))
Surface Tension given Critical Temperature
Go Surface Tension of Fluid given Critical Temp = Constant for each Liquid*(1-(Temperature/Critical Temperature))^(Empirical Factor)
Surface Tension given Correction Factor
Go Surface Tension of Fluid = (Drop Weight*[g])/(2*pi*Capillary Radius*Correction Factor)
Surface Tension given Molar Volume
Go Surface Tension of Fluid given Molar Volume = [EOTVOS_C]*(Critical Temperature-Temperature)/(Molar Volume)^(2/3)
Height of Magnitude of Capillary Rise
Go Height of Capillary Rise/Fall = Surface Tension of Fluid/((1/2)*(Radius of Tubing*Density of Fluid*[g]))
Surface Tension Force given Density of Fluid
Go Surface Tension of Fluid = (1/2)*(Radius of Tubing*Density of Fluid*[g]*Height of Capillary Rise/Fall)
Total Weight of Plate using Wilhelmy-Plate Method
Go Total Weight of Solid Surface = Weight of Plate+Surface Tension of Fluid*(Perimeter)-Upward Drift
Total Weight of Ring using Ring-Detachment Method
Go Total Weight of Solid Surface = Weight of Ring+(4*pi*Radius of Ring*Surface Tension of Fluid)
Parachor given Surface Tension
Go Parachor = (Molar Mass/(Density of Liquid-Density of Vapor))*(Surface Tension of Fluid)^(1/4)
Surface Pressure using Wilhelmy-Plate Method
Go Surface Pressure of Thin Film = -(Change in Force/(2* (Thickness of Plate+Weight of Plate)))
Surface Tension given Temperature
Go Surface Tension of Fluid given Temperature = 75.69-(0.1413*Temperature)-(0.0002985*(Temperature)^2)
Surface Pressure
Go Surface Pressure of Thin Film = Surface Tension of Clean Water Surface-Surface Tension of Fluid
Work of Cohesion given Surface Tension
Go Work of Cohesion = 2*Surface Tension of Fluid*[Avaga-no]^(1/3)*(Molar Volume)^(2/3)
Surface Tension for very Thin Plate using Wilhelmy-Plate Method
Go Surface Tension of Fluid = Force on very Thin Plate/(2*Weight of Plate)

Force given Surface Tension using Wilhelmy-Plate Method Formula

Force = (Density of Plate*[g]*(Length of Plate*Width of Full Size Bearing Plate*Thickness of Plate))+(2*Surface Tension of Fluid*(Thickness of Plate+Width of Full Size Bearing Plate)*(cos(Contact Angle)))-(Density of Fluid*[g]*Thickness of Plate*Width of Full Size Bearing Plate*Depth of Plate)
F = (ρp*[g]*(L*B*t))+(2*γ*(t+B)*(cos(θ)))-(ρfluid*[g]*t*B*hp)

What is Wilhelmy-Plate Method?

The Wilhelmy plate method for measuring interfacial tension uses a Wilhelmy plate that is pulled upward or pushed downward through an interface. In this method, the plate is oriented perpendicular to the interface, and the force exerted on it is measured.

How to Calculate Force given Surface Tension using Wilhelmy-Plate Method?

Force given Surface Tension using Wilhelmy-Plate Method calculator uses Force = (Density of Plate*[g]*(Length of Plate*Width of Full Size Bearing Plate*Thickness of Plate))+(2*Surface Tension of Fluid*(Thickness of Plate+Width of Full Size Bearing Plate)*(cos(Contact Angle)))-(Density of Fluid*[g]*Thickness of Plate*Width of Full Size Bearing Plate*Depth of Plate) to calculate the Force, The Force given Surface Tension using Wilhelmy-Plate Method formula is the net downward force which is expressed in dimensions of rectangular plate i.e., Lp and Wp and material density ρ, depth hp in a liquid of density ρL. Force is denoted by F symbol.

How to calculate Force given Surface Tension using Wilhelmy-Plate Method using this online calculator? To use this online calculator for Force given Surface Tension using Wilhelmy-Plate Method, enter Density of Plate (ρp), Length of Plate (L), Width of Full Size Bearing Plate (B), Thickness of Plate (t), Surface Tension of Fluid (γ), Contact Angle (θ), Density of Fluid (ρfluid) & Depth of Plate (hp) and hit the calculate button. Here is how the Force given Surface Tension using Wilhelmy-Plate Method calculation can be explained with given input values -> 4.2E+9 = (12.2*[g]*(0.05*0.2*5))+(2*0.073*(5+0.2)*(cos(0.263544717051094)))-(14.9*[g]*5*0.2*0.0121).

FAQ

What is Force given Surface Tension using Wilhelmy-Plate Method?
The Force given Surface Tension using Wilhelmy-Plate Method formula is the net downward force which is expressed in dimensions of rectangular plate i.e., Lp and Wp and material density ρ, depth hp in a liquid of density ρL and is represented as F = (ρp*[g]*(L*B*t))+(2*γ*(t+B)*(cos(θ)))-(ρfluid*[g]*t*B*hp) or Force = (Density of Plate*[g]*(Length of Plate*Width of Full Size Bearing Plate*Thickness of Plate))+(2*Surface Tension of Fluid*(Thickness of Plate+Width of Full Size Bearing Plate)*(cos(Contact Angle)))-(Density of Fluid*[g]*Thickness of Plate*Width of Full Size Bearing Plate*Depth of Plate). The Density of Plate is the ratio of the mass of the plate to its volume, Length of Plate is the distance between two extreme points along one side of the base plate, Width of Full Size Bearing Plate is the smaller dimension of plate, Thickness of Plate is defined as the thickness of plate (usually the lowest dimension of the plate) under consideration, Surface Tension of Fluid is the energy or work required to increase the surface area of a fluid due to intermolecular forces, The Contact Angle is an angle that a liquid creates with a solid surface or capillary walls of a porous material when both materials come in contact together, Density of Fluid is defined as the mass of fluid per unit volume of the said fluid & Depth of Plate is a dimension taken through the surface of the plate, usually downward from an upper surface, horizontally inward from an outer surface.
How to calculate Force given Surface Tension using Wilhelmy-Plate Method?
The Force given Surface Tension using Wilhelmy-Plate Method formula is the net downward force which is expressed in dimensions of rectangular plate i.e., Lp and Wp and material density ρ, depth hp in a liquid of density ρL is calculated using Force = (Density of Plate*[g]*(Length of Plate*Width of Full Size Bearing Plate*Thickness of Plate))+(2*Surface Tension of Fluid*(Thickness of Plate+Width of Full Size Bearing Plate)*(cos(Contact Angle)))-(Density of Fluid*[g]*Thickness of Plate*Width of Full Size Bearing Plate*Depth of Plate). To calculate Force given Surface Tension using Wilhelmy-Plate Method, you need Density of Plate (ρp), Length of Plate (L), Width of Full Size Bearing Plate (B), Thickness of Plate (t), Surface Tension of Fluid (γ), Contact Angle (θ), Density of Fluid (ρfluid) & Depth of Plate (hp). With our tool, you need to enter the respective value for Density of Plate, Length of Plate, Width of Full Size Bearing Plate, Thickness of Plate, Surface Tension of Fluid, Contact Angle, Density of Fluid & Depth of Plate and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Force?
In this formula, Force uses Density of Plate, Length of Plate, Width of Full Size Bearing Plate, Thickness of Plate, Surface Tension of Fluid, Contact Angle, Density of Fluid & Depth of Plate. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Force = Weight of Plate+(Surface Force*((Surface Tension of Fluid*Perimeter of Plate)-Upward Drift))
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