One means by which a nozzle can be forced to operate at maximum thrust or "on design" under many different flight conditions is through a.variable geometry. For such a nozzle, the area of the exit, throat, or both is varied so that the optimum exit pressure can be obtained. Two nozzle shapes are usually used: a simple circular (iris) nozzle or a plug nozzle. Note that variable nozzles are typically not used on commercial aircraft because of the limited flight envelope -that is, the craft and engine basically are optimally designed for one altitude and flight condition. Military fighters, on the other hand, must be designed to operate under a variety of conditions, including aircraft carrier takeoff. As a result, most of these engines have variable nozzles.
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There are two possible ways: The first is to obtain a formula for the area which depends on a variable (the base). For example, consider all triangles with a base of x cm and a height of 4 cm. What is their area? Answer: it is 1/2*height*base = 1/2*4*x = 2x cm2. So I have an answer which includes the variable representing the base. The second possibility is that there is supplementary information that allows you (if you work hard enough) to find a value for the base.
1. Elimination: Select two equations and a variable to eliminate. Multiply each equation by the coefficient if that variable in the other equation. If the signs of the coefficient for that variable in the resulting equations are the same then subtract one new equation from the other. If they have opposite signs then add them. You will now have an equation without that variable. Repeat will other pairs and you will end up with one fewer equation and one fewer variable. Repeat this process: after each round you will have one fewer equation and one fewer variable. Keep going until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.2. Substitution: Select a equation and a variable. Make that variable the subject of the equation. The right hand side of this equation is an expression for that variable. Substitute this expression for the variable is each of the other equations. Again, one fewer equation in one fewer variable. Continue until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.3. Matrix inversion: If A is the nxn matrix of coefficients, X is the nx1 [column] matrix of variables and B is the nx1 matrix of the equation constants, then X = A^-1*B where A^-1 is the inverse of matrix A.
An independent variable is basically a variable that can be any number. The dependent variable is the variable calculated from the independent variable. For example, I do contract work where I get paid for every hour of work I do in a given week. If I work more hours, my paycheck is bigger. So in this case the number of hours I work is the independent variable (it can, in theory, be anywhere from 0 to 40 or more hours each week), and the dependent variable is the amount on my paycheck (it is a variable too, but it directly depends on the number of hours I worked).
A discrete variable is a variable that has a certain set limit. For example, a ten point scale can ONLY have the variables 1, 2, 3, 4, 5, 6, 7, 8, 9, & 10. 2.8 would not work on a discrete variable ten point scale. Height is an example of a continuous variable, or one that has an infinite possibility.
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