Variation of y with x in Free Liquid Jet Calculator

✖Length x is simply the distance from the origin to the x coordinate.ⓘ Length x [x]			+10% -10%
✖The Angle of Liquid Jet is defined as the angle between the horizontal x-axis and the free liquid jet.ⓘ Angle of Liquid Jet [Θ]			+10% -10%
✖The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖The initial velocity of liquid jet is defined as the velocity possed by the liquid jet at time T=0.ⓘ Initial Velocity of Liquid Jet [V_o]			+10% -10%

✖Length y is the vertical distance from the origin to the y coordinate.ⓘ Variation of y with x in Free Liquid Jet [y]

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Formula

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Variation of y with x in Free Liquid Jet

Formula

`"y" = "x"*tan("Θ")-("g"*"x"^2*sec("Θ"))/(2*"V"_{"o"}^2)`

Example

`"0.199894m"="0.2m"*tan("45°")-("9.8m/s²"*("0.2m")^2*sec("45°"))/(2*("51.2m/s")^2)`

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Variation of y with x in Free Liquid Jet Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length y = Length x*tan(Angle of Liquid Jet)-(Acceleration due to Gravity*Length x^2*sec(Angle of Liquid Jet))/(2*Initial Velocity of Liquid Jet^2)
y = x*tan(Θ)-(g*x^2*sec(Θ))/(2*V_o^2)
This formula uses 2 Functions, 5 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)

Variables Used

Length y - (Measured in Meter) - Length y is the vertical distance from the origin to the y coordinate.
Length x - (Measured in Meter) - Length x is simply the distance from the origin to the x coordinate.
Angle of Liquid Jet - (Measured in Radian) - The Angle of Liquid Jet is defined as the angle between the horizontal x-axis and the free liquid jet.
Acceleration due to Gravity - (Measured in Meter per Square Second) - The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Initial Velocity of Liquid Jet - (Measured in Meter per Second) - The initial velocity of liquid jet is defined as the velocity possed by the liquid jet at time T=0.

STEP 1: Convert Input(s) to Base Unit

Length x: 0.2 Meter --> 0.2 Meter No Conversion Required
Angle of Liquid Jet: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Initial Velocity of Liquid Jet: 51.2 Meter per Second --> 51.2 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y = x*tan(Θ)-(g*x^2*sec(Θ))/(2*V_o^2) --> 0.2*tan(0.785398163397301)-(9.8*0.2^2*sec(0.785398163397301))/(2*51.2^2)

Evaluating ... ...

y = 0.199894261986397

STEP 3: Convert Result to Output's Unit

0.199894261986397 Meter --> No Conversion Required

FINAL ANSWER

0.199894261986397 ≈ 0.199894 Meter <-- Length y

(Calculation completed in 00.004 seconds)

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Variation of y with x in Free Liquid Jet

Go Length y = Length x*tan(Angle of Liquid Jet)-(Acceleration due to Gravity*Length x^2*sec(Angle of Liquid Jet))/(2*Initial Velocity of Liquid Jet^2)

Initial Velocity of Liquid Jet given Maximum Vertical Elevation

Go Initial Velocity of Liquid Jet = sqrt(Maximum Vertical Elevation*2*Acceleration due to Gravity/(sin(Angle of Liquid Jet)*sin(Angle of Liquid Jet)))

Maximum Vertical Elevation of Jet Profile

Go Maximum Vertical Elevation = (Initial Velocity of Liquid Jet^(2)*sin(Angle of Liquid Jet)*sin(Angle of Liquid Jet))/(2*Acceleration due to Gravity)

Angle of Jet given Maximum Vertical Elevation

Go Angle of Liquid Jet = asin(sqrt((Maximum Vertical Elevation*2*Acceleration due to Gravity)/Initial Velocity of Liquid Jet^(2)))

Initial Velocity given Time to Reach Highest Point of Liquid

Go Initial Velocity of Liquid Jet = Time to Reach Highest Point*Acceleration due to Gravity/sin(Angle of Liquid Jet)

Angle of Jet given Time of Flight of Liquid Jet

Go Angle of Liquid Jet = asin(Time of Flight*Acceleration due to Gravity/(2*Initial Velocity of Liquid Jet))

Time of Flight of Jet

Go Time of Flight = (2*Initial Velocity of Liquid Jet*sin(Angle of Liquid Jet))/Acceleration due to Gravity

Angle of Jet given Time to Reach Highest Point

Go Angle of Liquid Jet = asin(Time of Flight*Acceleration due to Gravity/(Initial Velocity of Liquid Jet))

Initial Velocity given Time of Flight of Liquid Jet

Go Initial Velocity of Liquid Jet = Time of Flight*Acceleration due to Gravity/(sin(Angle of Liquid Jet))

Horizontal Range of Jet

Go Range = Initial Velocity of Liquid Jet^(2)*sin(2*Angle of Liquid Jet)/Acceleration due to Gravity

Mean Velocity given Frictional Velocity

Go Mean Velocity = Friction Velocity/sqrt(Friction Factor/8)

Friction Velocity

Go Friction Velocity = Mean Velocity*sqrt(Friction Factor/8)

Variation of y with x in Free Liquid Jet Formula

Length y = Length x*tan(Angle of Liquid Jet)-(Acceleration due to Gravity*Length x^2*sec(Angle of Liquid Jet))/(2*Initial Velocity of Liquid Jet^2)
y = x*tan(Θ)-(g*x^2*sec(Θ))/(2*V_o^2)

What is a free liquid jet?

The free liquid jet is basically defined as the jet of fluid coming out from the nozzle in the atmosphere. The path traveled by the free jet is parabolic and this is called as a projectile.

How to Calculate Variation of y with x in Free Liquid Jet?

Variation of y with x in Free Liquid Jet calculator uses Length y = Length x*tan(Angle of Liquid Jet)-(Acceleration due to Gravity*Length x^2*sec(Angle of Liquid Jet))/(2*Initial Velocity of Liquid Jet^2) to calculate the Length y, Variation of y with x in Free Liquid Jet simply discribes the variation of the vertical displacement of liquid jet with respective to the horizontal displacement. Length y is denoted by y symbol.

How to calculate Variation of y with x in Free Liquid Jet using this online calculator? To use this online calculator for Variation of y with x in Free Liquid Jet, enter Length x (x), Angle of Liquid Jet (Θ), Acceleration due to Gravity (g) & Initial Velocity of Liquid Jet (V_o) and hit the calculate button. Here is how the Variation of y with x in Free Liquid Jet calculation can be explained with given input values -> 0.199894 = 0.2*tan(0.785398163397301)-(9.8*0.2^2*sec(0.785398163397301))/(2*51.2^2).

FAQ

What is Variation of y with x in Free Liquid Jet?

Variation of y with x in Free Liquid Jet simply discribes the variation of the vertical displacement of liquid jet with respective to the horizontal displacement and is represented as y = x*tan(Θ)-(g*x^2*sec(Θ))/(2*V_o^2) or Length y = Length x*tan(Angle of Liquid Jet)-(Acceleration due to Gravity*Length x^2*sec(Angle of Liquid Jet))/(2*Initial Velocity of Liquid Jet^2). Length x is simply the distance from the origin to the x coordinate, The Angle of Liquid Jet is defined as the angle between the horizontal x-axis and the free liquid jet, The Acceleration due to Gravity is acceleration gained by an object because of gravitational force & The initial velocity of liquid jet is defined as the velocity possed by the liquid jet at time T=0.

How to calculate Variation of y with x in Free Liquid Jet?

Variation of y with x in Free Liquid Jet simply discribes the variation of the vertical displacement of liquid jet with respective to the horizontal displacement is calculated using Length y = Length x*tan(Angle of Liquid Jet)-(Acceleration due to Gravity*Length x^2*sec(Angle of Liquid Jet))/(2*Initial Velocity of Liquid Jet^2). To calculate Variation of y with x in Free Liquid Jet, you need Length x (x), Angle of Liquid Jet (Θ), Acceleration due to Gravity (g) & Initial Velocity of Liquid Jet (V_o). With our tool, you need to enter the respective value for Length x, Angle of Liquid Jet, Acceleration due to Gravity & Initial Velocity of Liquid Jet and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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