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Fluid Force Evaluate the following two
(a)
(b)
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- Seawater has density 1025 kg/m³ and flows in a velocity field v = yi + x j, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x2 + y2 + z2 = 64, z 2 0. kg/sarrow_forwardDetermine the type of points on the X (u, v) = (u, v, u?) surface. Differential geometryarrow_forwardStokes' Theorem (1.50) Given F = x²yi – yj. Find (a) V x F (b) Ss F- da over a rectangle bounded by the lines x = 0, x = b, y = 0, and y = c. (c) fc ▼ x F. dr around the rectangle of part (b).arrow_forward
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- Coulomb's Law states that the force of attraction between two charged particles is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The figure shows particles with charge 1 located at positions 0 and 2 on a coordinate line and a particle with charge −1 at a position x between them. It follows from Coulomb's Law that the net force acting on the middle particle isarrow_forwardCalculate the line integral of the vector field F = (y, x,x² + y² ) around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field. The surface S is the upper hemisphere x² + y + z? = 25, z 2 0 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) F. dr = curl(F) =arrow_forwardдм Consider the equation (y2 – 2x)dx + (2xy+ 1)dy = 0. If f(x, y) ON what is the value of əx ду f(1,2)? A -1 В 2 (D 1arrow_forward
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