Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam Calculator

✖Thrust from water retained behind a wall is the force applied by the water on unit length of wall.ⓘ Thrust from Water [P]			+10% -10%
✖Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.ⓘ Thrust of Abutments [F]			+10% -10%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ]			+10% -10%
✖Radius to Center Line of Arch is a radial line from the focus to any point of a curve.ⓘ Radius to Center Line of Arch [r]			+10% -10%

✖Radial pressure is a pressure towards or away from the central axis of a component.ⓘ Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam [P_v]

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Formula

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Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam

Formula

`"P"_{"v"} = (("P"+"F"*cos("θ"))/("r"-("r"*cos("θ"))))`

Example

`"21.78844kPa/m²"=(("16kN/m"+"63.55N"*cos("30°"))/("5.5m"-("5.5m"*cos("30°"))))`

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Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radial Pressure = ((Thrust from Water+Thrust of Abutments*cos(Theta))/(Radius to Center Line of Arch-(Radius to Center Line of Arch*cos(Theta))))
P_v = ((P+F*cos(θ))/(r-(r*cos(θ))))
This formula uses 1 Functions, 5 Variables

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

Radial Pressure - (Measured in Pascal per Square Meter) - Radial pressure is a pressure towards or away from the central axis of a component.
Thrust from Water - (Measured in Newton per Meter) - Thrust from water retained behind a wall is the force applied by the water on unit length of wall.
Thrust of Abutments - (Measured in Newton) - Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
Radius to Center Line of Arch - (Measured in Meter) - Radius to Center Line of Arch is a radial line from the focus to any point of a curve.

STEP 1: Convert Input(s) to Base Unit

Thrust from Water: 16 Kilonewton per Meter --> 16000 Newton per Meter (Check conversion here)
Thrust of Abutments: 63.55 Newton --> 63.55 Newton No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Radius to Center Line of Arch: 5.5 Meter --> 5.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_v = ((P+F*cos(θ))/(r-(r*cos(θ)))) --> ((16000+63.55*cos(0.5235987755982))/(5.5-(5.5*cos(0.5235987755982))))

Evaluating ... ...

P_v = 21788.4399090629

STEP 3: Convert Result to Output's Unit

21788.4399090629 Pascal per Square Meter -->21.7884399090629 Kilopascal per Square Meter (Check conversion here)

FINAL ANSWER

21.7884399090629 ≈ 21.78844 Kilopascal per Square Meter <-- Radial Pressure

(Calculation completed in 00.004 seconds)

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< 4 Normal Radial Pressure of Arch Dams Calculators

Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam

Go Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*((sin(Theta)/(Theta))-cos(Theta))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*((sin(Theta)/(Theta))-cos(Theta)))

Normal Radial Pressure at centerline given Moment at Crown of Arch Dam

Go Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*(1-(sin(Theta)/(Theta)))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*(1-(sin(Theta)/(Theta))))

Normal Radial Pressure at centerline given Thrust at Crown of Arch Dam

Go Radial Pressure = Thrust at Crown/((Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Horizontal Thickness of an Arch/Radius to Center Line of Arch)^2)/12)/Diameter)))

Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam

Go Radial Pressure = ((Thrust from Water+Thrust of Abutments*cos(Theta))/(Radius to Center Line of Arch-(Radius to Center Line of Arch*cos(Theta))))

Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam Formula

Radial Pressure = ((Thrust from Water+Thrust of Abutments*cos(Theta))/(Radius to Center Line of Arch-(Radius to Center Line of Arch*cos(Theta))))
P_v = ((P+F*cos(θ))/(r-(r*cos(θ))))

What is Arch Dam ?

An arch dam is a concrete dam that is curved upstream in plan. The arch dam is designed so that the force of the water against it, known as hydrostatic pressure, presses against the arch, causing the arch to straighten slightly and strengthening the structure as it pushes into its foundation or abutments.

How to Calculate Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam?

Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam calculator uses Radial Pressure = ((Thrust from Water+Thrust of Abutments*cos(Theta))/(Radius to Center Line of Arch-(Radius to Center Line of Arch*cos(Theta)))) to calculate the Radial Pressure, Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam is defined as as pressure exerted due to water on dam. Radial Pressure is denoted by P_v symbol.

How to calculate Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam using this online calculator? To use this online calculator for Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam, enter Thrust from Water (P), Thrust of Abutments (F), Theta (θ) & Radius to Center Line of Arch (r) and hit the calculate button. Here is how the Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam calculation can be explained with given input values -> 0.021788 = ((16000+63.55*cos(0.5235987755982))/(5.5-(5.5*cos(0.5235987755982)))).

FAQ

What is Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam?

Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam is defined as as pressure exerted due to water on dam and is represented as P_v = ((P+F*cos(θ))/(r-(r*cos(θ)))) or Radial Pressure = ((Thrust from Water+Thrust of Abutments*cos(Theta))/(Radius to Center Line of Arch-(Radius to Center Line of Arch*cos(Theta)))). Thrust from water retained behind a wall is the force applied by the water on unit length of wall, Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments, Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint & Radius to Center Line of Arch is a radial line from the focus to any point of a curve.

How to calculate Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam?

Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam is defined as as pressure exerted due to water on dam is calculated using Radial Pressure = ((Thrust from Water+Thrust of Abutments*cos(Theta))/(Radius to Center Line of Arch-(Radius to Center Line of Arch*cos(Theta)))). To calculate Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam, you need Thrust from Water (P), Thrust of Abutments (F), Theta (θ) & Radius to Center Line of Arch (r). With our tool, you need to enter the respective value for Thrust from Water, Thrust of Abutments, Theta & Radius to Center Line of Arch 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 Radial Pressure?

In this formula, Radial Pressure uses Thrust from Water, Thrust of Abutments, Theta & Radius to Center Line of Arch. We can use 3 other way(s) to calculate the same, which is/are as follows -

Radial Pressure = Thrust at Crown/((Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Horizontal Thickness of an Arch/Radius to Center Line of Arch)^2)/12)/Diameter)))
Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*(1-(sin(Theta)/(Theta)))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*(1-(sin(Theta)/(Theta))))
Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*((sin(Theta)/(Theta))-cos(Theta))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*((sin(Theta)/(Theta))-cos(Theta)))

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