In this figure,an ideal liquid flows through a tube of uniform cross-section. The liquid has velocities $v_A$ and $v_B$,and pressures $P_A$ and $P_B$ at points $A$ and $B$ respectively.

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

$Assertion :$ The velocity of flow of a liquid is smaller when pressure is larger and vice-versa.
$Reason :$ According to Bernoulli's theorem,for the stream line flow of an ideal liquid,the total energy per unit mass remains constant.

$A$ horizontal pipe carries water in a streamlined flow. At a point along the pipe,where the cross-sectional area is $10 \text{ cm}^2$,the velocity of water is $1 \text{ ms}^{-1}$ and the pressure is $2000 \text{ Pa}$. What is the pressure of water at another point where the cross-sectional area is $5 \text{ cm}^2$ (in $Pa$)? [Density of water $= 1000 \text{ kgm}^{-3}$]

Explain with the help of Bernoulli's principle why a spinning ball follows a curved path during flight.

Water flows in a horizontal tube (see figure). The pressure of water changes by $700 \; Nm^{-2}$ between $A$ and $B$ where the area of cross-section are $40 \; cm^{2}$ and $20 \; cm^{2},$ respectively. Find the rate of flow of water through the tube in $cm^{3} / s$. (Density of water $= 1000 \; kgm^{-3}$)