Question 32171
WATER FLOW QUANTITY,AREA FOR FLOW AND THE VELOCTY OF FLOW ARE THE 3 QUANTITIES INVOLVED,LEAVING ASIDE....RESISTANCE TO FLOW, WATER PRESSURE,ITS DROP ETC..FOR THE MOMENT TO SIMPLIFY THE UNDERSTANDING;THOUGH THEY ARE REQUIRED FOR MORE RIGOROUS APPROACH.
THE 3 ARE CONNECTED BY 
Q=WATER FLOW IN CC/SEC OR GALLONS/SEC OR WHATEVER UNIT 
A=AREA OF CROSS SECTION OF HOSE..IN SQUARE CM..OR SQUARE FT..ETC..
V=VELOCITY OF FLOW...IN M/SEC OR FT/SEC ETC..
Q=AV....OR......V=Q/A
SO WHEN YOU ARE PARTIALLY CLOSING THE HOSE, AREA IS REDUCED WHERE AS FLOW IS ALMOST  SAME ASSUMING SUFFICIENT PRESSURE IN THE HOSE..SO..WE HAVE
V=Q (ALMOST SAME OR A LITTLE LESS)/A (REDUCED CONSIDERABLY)=INCREASE IN VALUE...THAT IS VELOCITY INCREASES.THAT EXPLAINS YOUR OBSERVATION.BUT YOUR OTHER DOUBT IS ALSO PROVED CORRECT IF YOU CONTINUE TO PRESS THE HOSE TILL AREA AVAILABLE IS ZERO,THEN FLOW STOPS OR V=0..SINCE NOW THE OTHER FACTORS MENTIONED ABOVE COME INTO PLAY AND THE PRESURE OF WATER AVAILABLE IN THE HOSE IS TOTALLY OFFSET BY THE RESISTANCE IMPOSED.