why we use euler equation in fluid mechanics
1.Why should we study fluid mechanics? 2.What's a Fluid mechanics? 3.What's a Fluid? 4,What's difference between a solid and a fluid ? 5.What is the difference between a unit and a dimension? 6.Which terms in equation are dimensionally homogeneous? 2ma 7.What is Density? 8.What is Specific Weight? 9.What is Specific Gravity? 10.What is Specific Volume? 11. What is the ideal gas equation of state?
Evaluate the double integral ∫∫D x cos y dA, where D is bounded by x = 0, y = x², and x = 3 Answer:
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z. 1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
Explain in words why we need to introduce the stress tensor for fluid mechanics.
Evaluate the given integral by changing to polar coordinates. ∫∫R(4x − y) dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x.
3. (1.5 points) Evaluate the integral using a change of variables. (x + y)ez?-y dA JJR where R is the polygon with vertices (1,0), (0, 1), (-1,0), and (0, -1).
Calculate the double integral ||(x + 3 y) dA where R is bounded by y = Vx and y = x
Evaluate the integral using a change of variables. Z ZR (x + y) sin(x − y) dA (Z's are integrals) where R is the triangular region with vertices (−1, 1), (1, 1), and (0, 0).
1) Given the following iterated integral. ex/Y DA R = y = 4x, y = -xy = 8 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (1.25 point) Evaluate the definite integral with the given function over the bounded region R.