Water is flowing in a pipe of diameter $4 \text{ cm}$ with a velocity $3 \text{ m/s}$. The water then enters into a tube of diameter $2 \text{ cm}$. The velocity of water in the other pipe is .......... $\text{m/s}$.

The cylindrical tube of a spray pump has radius $R,$ one end of which has $n$ fine holes,each of radius $r.$ If the speed of the liquid in the tube is $v,$ the speed of the ejection of the liquid through the holes is

Water enters through end $A$ with speed $v_1$ and leaves through end $B$ with speed $v_2$ of a cylindrical tube $AB$. The tube is always completely filled with water. In case $I$,the tube is horizontal; in case $II$,it is vertical with end $A$ upwards; and in case $III$,it is vertical with end $B$ upwards. We have $v_1 = v_2$ for:

Define line of flow and streamline.

The Bhagirathi and the Alaknanda merge at Deoprayag to form the Ganga. The speeds of the Bhagirathi and the Alaknanda are in the ratio $1: 1.5$. The cross-sectional areas of the Bhagirathi,the Alaknanda,and the Ganga are in the ratio $1: 2: 3$. Assuming streamline flow,the ratio of the speed of the Ganga to that of the Alaknanda is

In the figure shown,a liquid is flowing through a tube at the rate of $0.1\, m^3/sec$. The tube is branched into two semicircular tubes of cross-sectional area $A/3$ and $2A/3$. The velocity of liquid at $Q$ is ......... $m/sec$. (The cross-section of the main tube $= A = 10^{-2}\, m^2$ and $v_p = 20\, m/sec$)