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5. Consider a steady two-dimensional flow in the (x1, x2)-plane of a Newtonian, incompressible and inviscid liquid of density p with a free surface. The ambient gas is inviscid, and its pressure is constant and is equal to po. The only external force (per unit volume) acting on the liquid is the gravity force F = -pgoi2, where go is the gravity constant and i2 is the unit vector along the x2-axis. The shape of the free surface is given, which satisfies T2(x1) = exp(-(x1 – a0)²). Determine distribution of velocity amplitude u and pressure p as a function of x1 along the free surface, if at x1 → -0o the velocity is uo = (1, 0). Determine the minimum value of the velocity at the free surface.

5. Consider a steady two-dimensional flow in the (x1, x2)-plane of a Newtonian, incompressible and inviscid liquid of density p with a free surface. The ambient gas is inviscid, and its pressure is constant and is equal to po. The only external force (per unit volume) acting on the liquid is the gravity force F = -pgoi2, where go is the gravity constant and i2 is the unit vector along the x2-axis. The shape of the free surface is given, which satisfies T2(x1) = exp(-(x1 – a0)²). Determine distribution of velocity amplitude u and pressure p as a function of x1 along the free surface, if at x1 → -0o the velocity is uo = (1, 0). Determine the minimum value of the velocity at the free surface.

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5. Consider a steady two-dimensional flow in the (x1, x2)-plane of a Newtonian, incompressible and inviscid liquid of density p with a free surface. The ambient gas is inviscid, and its pressure is constant and is equal to po. The only external force (per unit volume) acting on the liquid is the gravity force F = -pgoi2, where go is the gravity constant and i2 is the unit vector along the x2-axis. The shape of the free surface is given, which satisfies x2(x1) = exp(-(x1 – a0)²). Determine distribution of velocity amplitude and pressure p as a function of x1 along the free surface, if at x1 → -o the velocity is U. Determine the minimum value of the velocity at the free surface. (1,0).
Transcribed Image Text:5. Consider a steady two-dimensional flow in the (x1, x2)-plane of a Newtonian, incompressible and inviscid liquid of density p with a free surface. The ambient gas is inviscid, and its pressure is constant and is equal to po. The only external force (per unit volume) acting on the liquid is the gravity force F = -pgoi2, where go is the gravity constant and i2 is the unit vector along the x2-axis. The shape of the free surface is given, which satisfies x2(x1) = exp(-(x1 – a0)²). Determine distribution of velocity amplitude and pressure p as a function of x1 along the free surface, if at x1 → -o the velocity is U. Determine the minimum value of the velocity at the free surface. (1,0).
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