Consider the velocity potential phi = -k( y^2 - x^2 ) where k is a constant....

Consider the velocity potential phi = -k( y^2 - x^2 ) where k is a constant. This velocity potential is commonly used to describe flow impinging upon a plate. Derive an equation for dP/dy, the pressure gradient in the y-direction, if the fluid has density, rho.

Expert Solution

samet mamat answered 2 years ago

Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The...

Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The point (0, 0) is a stationary point of f. For what values of k will f have a local minimum at (0, 0)? (a) |k| > 4 (b) k ≥ −4 (c) k ≤ 4 (d) |k| < 4 (e) none of the above The point P : (2, 2) is a stationary point of the function f(x, y) = 6xy − x ^3...

Consider the equation x^2+(y-2)^2 and the relation “(x, y) R (0, 2)”, where R is read...

Consider the equation x^2+(y-2)^2 and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “(x, y) belongs to the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation if, and only if, (x, y) R (0, 2)”. Does this equation determine a...

y''−2xy' + λy = 0, −∞ < x < ∞ where λ is a constant, is...

y''−2xy' + λy = 0, −∞ < x < ∞ where λ is a constant, is known as the Hermite equation, named after the famous mathematician Charles Hermite. This equation is an important equation in mathematical physics. • Find the ﬁrst four terms in each of two solutions about x = 0 and show that they form a fundamental set of solutions • Observe that if λ is a nonnegative even integer, then one or the other of the series...

Consider an economy where the velocity of the monetary base is assumed constant but nominal GDP...

Consider an economy where the velocity of the monetary base is assumed constant but nominal GDP grows 3 percent per annum. Is it possible for velocity to stay constant when money growth increases? 3. Assume the Ghanaian economy, in a particular year, has the following numbers in billions of Ghana Cedis: GDP = 400 Government consumption = 100 Transfers from the government to the private sector = 80 Government investment = 12 Government net interest payment = 8 Government production...

Consider the Cobb-Douglas production function Y = eb0 K b1 Lb2 eui where Y, K and...

Consider the Cobb-Douglas production function Y = eb0 K b1 Lb2 eui where Y, K and L denote real output, real capital input, and real labor input, respectively. The data for estimating the parameters of the production function are given in the Excel data file productionfunction.xls. Perform a logarithmic transformation of the production function to linearity so that it can be estimated by OLS. Compute the correlation coefficient between income lnK and lnL and comment on the potential for multicollinearity....

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers (a) Derive an equation...

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers (a) Derive an equation for a line tangent to both of these parabolas (show all steps with a proof, assuming that such a line exists) (b) Assume that the doubly-tangent line has an equation y+Ax+B. Find an example of values of a,b,c (other than the ones given here) such that A,B ∈ Z

Consider walks in the X-Y plane where each step is R: (x, y)→(x+1, y) or U:...

Consider walks in the X-Y plane where each step is R: (x, y)→(x+1, y) or U: (x, y)→(x, y+a), with a a positive integer. There are five walks that contain a point on the line x + y = 2, namely: RR, RU1, U1R, U1U1, and U2. Let a_n denote the number of walks that contain a point on the line x + y = n (so a_2 = 5). Show that a_n = F_{2n}, where F_n are the Fibonacci numbers...

A velocity field is described by the following equations: ?? = 10y/(x^2 +y^2) , ?? =...

A velocity field is described by the following equations: ?? = 10y/(x^2 +y^2) , ?? = -10x/(x^2+y^2) , and w=0 (a) Is this flow compressible or incompressible? (b) Find the pressure gradient. Assume frictionless flow in the z-axis, the density is 1.2 kg/m3 , and the z-axis is aligned with gravity. Also assume the normal and shear effects are negligible.

Let u(x, y) = x^3 + kxy^2 + y. (a) Determine the value of k such...

Let u(x, y) = x^3 + kxy^2 + y. (a) Determine the value of k such that u is an harmonic function. (b) Find the harmonic conjugate v of u. (c) Obtain the expression of f = u + iv in terms of z = x + iy

Assume that in Country X, the velocity of money is constant. Read GDP grows at 2%...

Assume that in Country X, the velocity of money is constant. Read GDP grows at 2% per year and the money stock grows at 10% per year. Let’s assume further that the nominal interest rate is equal to 12%. a. What is the growth rate of nominal GDP? b. What is the inflation rate? c. What is the real interest rate? What equations do you use to solve the following questions, please provide formulas of how it was set up...

Question