A velocity field is given by u = 5y2 and v = 2x a) Determine...

A velocity field is given by u = 5y\textsuperscript{2} and v = 2x a) Determine the streamline equation in the form: y = f(x) + c. b) Calculate the x and y components of the acceleration at the point (1,4). c) Describe the points where the flow is rotational and irrotational.

Transcript

00:02 The given value is v which is equal to x i plus x into x minus 1 multiple of y plus 1 okay so the explanation quarters step 1 the data given is the velocity field a so the formula is v which is equal to x i plus x multiple of x minus 1 multiple of y plus 1 multiple j okay so here to determine plus streamlines for minus 1 3 and minus 0 .5 and 3 .5 a cap so the next one is step number 2 that is the general equation of the velocity field is as follows is the gender equation which is that b is equal to u i plus b j okay so compare the general equation with the given value following equation of the velocity field so we get here in the equation of b which is equal to x i plus x means to multiple of x minus 1 multiple of y plus 1 multiple y plus 1 multiple j so on comparing a, we get u which is equal to x, then b which is equal to x multiple of x minus 1 multiple of y plus 1.

02:00 Okay, so the next step is step number 3, that is from the definition of screen 9.

02:12 So 3 in 9 definition is d .y by d .y dividing bf, which is equal.

02:18 To b dividing u so the next value is divide dividing d x which is equal to x into x minus 1 multiple y plus 1 dividing x so therefore d y dividing d f which is equal to x minus 1 multiple y plus 1.

02:48 Okay so now solve the above differential equation as d .y dividing y plus 1 which is equal to x minus 1 multiple d x.

03:04 So integrate both sides we get the value of integrators the value we get y plus 1 this is equal to x squared dividing 2 minus x plus c okay so so then next one is apply boundary condition.

03:28 We get, we want to substitute x which is equal to 0 and then y which is equal to 0 means.

03:38 So integrate part of 0 plus 1 which is equal to 0 minus 0 plus 2.

03:44 So c which is equal to in multiple of 1...

Question

A velocity field is given by u = 5y\textsuperscript{2} and v = 2x a) Determine the streamline equation in the form: y = f(x) + c. b) Calculate the x and y components of the acceleration at the point (1,4). c) Describe the points where the flow is rotational and irrotational.

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