STATEMENT-1: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held down [2008]

Question

STATEMENT-1: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

STATEMENT-2: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant. [2008]

Smart Achievers · Accepted Answer

(1)

The volume flow rate (Q) of an incompressible fluid in steady flow remains constant.

From equation of continuity, $a v$ = constant

$∴$ $Q = a \times v = constant$ $or, a \propto \frac{1}{v}$

where $a$ = area of cross-section and $v$ = velocity

If $v$ decreases, $a$ increases and vice-versa.

When stream of water moves up, its speed $(v)$ decreases and therefore $' a'$ increases i.e. the water spreads out as a fountain. When stream of water from hose pipe moves down, its speed increases and therefore area of cross-section decreases.

Solution

1 Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

2 Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

3 Statement-1 is True, Statement-2 is False

4 Statement-1 is False, Statement-2 is True

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