Bernoulli's Law says that

$\displaystyle P + pgy + \frac{1}{2}pv^2 = \text{constant}$

We also have

$\displaystyle A_1v_1 = \text{constant}$

(Continuity equation)

Originally Posted by **werehk** For incompressible fluid in steady flow, when a pressure is applied,
would there be a change in speed of fluid? |

If we are applying a pressure then that pressure indicates a force from outside the system. The extra force per unit area on the fluid is certain to increase the speed of the flow.

Originally Posted by **werehk** When the cross section area is reduced, the speed rises, so would the pressure of fluid drops? |

From the continuity equation, when the cross sectional area drops, the speed must increase.

Thus from Bernoulli's equation the speed has increased meaning that the pressure must drop. (Assuming that the level of the fluid, y, remains unchanged.)

-Dan