A hose has been clamped so that the area at the clamp is only one quarter the area of the rest of the hose. When we ignore the viscosity of water, the ratio of the speed of the water through the clamped area to the speed of the water when it leaves the hose is
A) .
B) .
C)1.
D)2
E)4.

Question

A hose has been clamped so that the area at the clamp is only one quarter the area of the rest of the hose. When we ignore the viscosity of water, the ratio of the speed of the water through the clamped area to the speed of the water when it leaves the hose is
A) . 
B) . 
C)1. 
D)2 
E)4.

Quizplus · Accepted Answer

According to the principle of the continuity equation, the product of the area and the speed of flow of an incompressible fluid remains constant as it passes through a pipe or duct. Therefore, $A_1V_1=A_2V_2$, where $A_1$ and $A_2$ are the areas, and $V_1$ and $V_2$ are the speeds of the water flowing through the narrow and wide parts of the hose respectively. Let $A_2$ be the area of the wide part of the hose, then $A_1 = \frac{1}{4} A_2$. Therefore, $V_1 = 4V_2$, and the ratio of the speeds is $\frac{V_1}{V_2} = \boxed{	extbf{(E) }4}$.

A Hose Has Been Clamped So That the Area at the Clamp