Here, let's consider mass flux of water flowing with a vector velocity field, and we will assume that the water is incompressible with a fixed mass density p= 10 kg/m. We can then describe the water flow as this density times the velocity: f = pv. 1. Qir 1. First consider the fluid flow along the x-axis with a form: (1) Consider a square wire loop oriented in the yz-plane side length of s = 0.2 m. If vo = 1.0 m/s, what is the mass flow rate (m) through the loop, expressed in kg/s? 6) What is the mass flow if the same loop is oriented in xy-plane? f = We define the orientation of the loop in terms of the normal vector and we can define the vector area bounded by loop as having magnitude equal to the area of this loop and an orientation along this normal vector. In the first problem above: A = Ai and the second case has A = Ak. With this convention, we can calculate m = f. A puoi. c) What is the mass flow through a loop oriented with A = 0.2 mi+ 0.2 mj+0.2 mk? The key variable here is the surface that is bounded by the loop and not the loop length. If the same loop were stretched to be long and thin, the mass flow through the loop would be smaller: only the area matters. d) What is the mass flow from water with v0 = 2 m/s and f = puo 1 (1/ - 1/ + + 3 *) i- 3 3 through a surface that is a disk of radius r = 5 cm and area A = r 1 1 2