Characteristic Equations Q1.Reduce the following PDE equation to ODES(No need to solve them) in terms of...
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Characteristic Equations Q1.Reduce the following PDE equation to ODES(No need to solve them) in terms of y=y(x), u=u(x) and u=u(y) (a) (i) (iii) (iv) 3ux + 4 uy - 0 2ux + 5uy = 0 3ux + 2Uy = 0 1 5ux +4Uy = 0 PDE Q1. Express the total differential of Temperature (a) that varies across room in such a way that it is uniform along z-axis but varies in xy plane. (b) that varies across room in such a way that it is uniform along x-axis but varies in zy plane. (c) that varies across room in such a way that it is uniform along y-axis but varies in xz plane. Q2. Express the total differential of mass of fluid flowing in and out of tank via pump along (a) y-axis in such a way that width of water level in tank labeled by x-axis is increasing with a small leak of fluid outside tank along z-axis. 1 (b) z-axis in such a way that height of water level in tank labeled by y-axis is uniform with a small leak of fluid outside tank along x-axis. (c) x-axis in such a way that height of water level in tank labeled by y-axis is increasing with a small leak of fluid outside tank along z-axis. Characteristic Equations Q1.Reduce the following PDE equation to ODES(No need to solve them) in terms of y=y(x), u=u(x) and u=u(y) (a) (i) (iii) (iv) 3ux + 4 uy - 0 2ux + 5uy = 0 3ux + 2Uy = 0 1 5ux +4Uy = 0 PDE Q1. Express the total differential of Temperature (a) that varies across room in such a way that it is uniform along z-axis but varies in xy plane. (b) that varies across room in such a way that it is uniform along x-axis but varies in zy plane. (c) that varies across room in such a way that it is uniform along y-axis but varies in xz plane. Q2. Express the total differential of mass of fluid flowing in and out of tank via pump along (a) y-axis in such a way that width of water level in tank labeled by x-axis is increasing with a small leak of fluid outside tank along z-axis. 1 (b) z-axis in such a way that height of water level in tank labeled by y-axis is uniform with a small leak of fluid outside tank along x-axis. (c) x-axis in such a way that height of water level in tank labeled by y-axis is increasing with a small leak of fluid outside tank along z-axis.
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