$A$ venturimeter has a pipe diameter of $4 \,cm$ and a throat diameter of $2 \,cm$. The velocity of water in the pipe section is $10 \,m/s$. The pressure drop between the pipe section and the throat section is (use density of water $= 1000 \,kg/m^3$):

$A$ horizontal pipeline carries water in a stream-line flow. At a point along the pipe, where the cross-sectional area is $10 \,cm^2$, the velocity of water is $1 \,m/s$ and the pressure is $2000 \,Pa$. The pressure of water at another point where the cross-sectional area is $5 \,cm^2$ is (Given: density of water $\rho = 1000 \,kg/m^3$) (in $\,Pa$)

Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections $A, B$ and $C$ are shown. Sections $B$ and $C$ have equal area of cross-section. If $P_A, P_B$ and $P_C$ are the pressures at $A, B$ and $C$ respectively,then:

$A$ train with cross-sectional area $S_t$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S_0$ $(S_0 = 4S_t)$. Assume that almost all the air (density $\rho$) in front of the train flows back between its sides and the walls of the tunnel. Also,the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be $p_0$. If the pressure in the region between the sides of the train and the tunnel walls is $p$,then $p_0 - p = \frac{7}{2N} \rho v_t^2$. The value of $N$ is. . . . .

Prove Bernoulli's Principle.

Which of the following is not an assumption for an ideal fluid flow for which Bernoulli's principle is valid?