When we open a tap, the water flows down in a tapering manner (the width of the water column is broad near the tap and this decreases as it comes down). Do you know why

This is according to the law of Continuity.Acc. to this law A₁V₁=A₂V₂ . (Where A1,A2 are the area of the flow and V1,V2 are the velocities of Flow). Since while descending the velocity of water increases due to gravity thus the area of flow should decrease. Thats the reason why the water column is broad near  the top and its width decreases as it comes down.

"Since while descending the velocity of water increases due to gravity thus the area of flow should decrease."

How come?

Volume of water flowing through a given area in a given time must remain constant to maintain a streamlined flow. Since volume  of water flowing thorugh the area in a given time is equal to AV(A is area nd V is Velocity). Thus AV must remain constant. if V increases (due to gravity) A must decrease so as to keep the volum flowing through it constant 

Thanks for ur prompt reply.....

Can u give me ur gmail id? I want to talk to u personally...