The figure shows a non-viscous, incompressible and steady flow in front of a sphere. A-B is a horizontal streamline. It is known that the fluid velocity along this streamline is given by `V=V_(0)(1+(R^(3))/(x^(3))).V_(0)` is velocity of flow on this streamline when `xrarr(-oo)`. It is given that pressure at `xrarr(-oo)` is `P_(0)` and density of liquid is `rho`. (i) Write the variation of pressure along the streamline from pointA, far away from the sphere, to point B on the spehre. (ii) Plot the variation of pressure along the streamline from `x=-oo` to x=-R.

The figure shows a non-viscous, incompressible and steady flow in fron

1.	The figure shows a non-viscous, incompressible and steady flow in front of a sphere. A-B is a horizontal streamline. It is known that the fluid velocity along this streamline is given by `V=V_(0)(1+(R^(3))/(x^(3))).V_(0)` is velocity of flow on this streamline when `xrarr(-oo)`. It is given that pressure at `xrarr(-oo)` is `P_(0)` and density of liquid is `rho`. (i) Write the variation of pressure along the streamline from pointA, far away from the sphere, to point B on the spehre. (ii) Plot the variation of pressure along the streamline from `x=-oo` to x=-R.
Answer» Correct Answer - (i) `P=P_(0)+rhoV_(0)^(2)[1-(1_(R^(3))/(x^(3)))]`

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