Irodov Problem 1.319

Suppose that the hole is made at a height h. The fluid pressure P at this height is given by . Let the atmospheric pressure be Po.The water just to the left of the hole is assumed to be still, in other words it has no velocity.

Just to the right of the hole, say the water shoots out with a horizontal velocity v. The water coming out of the hole to enter a zone with pressure equal to atmospheric pressure and so from Bernoulli's equation we have,




Gravity pulls the water down with an acceleration of g, and so the time t taken by water to reach the surface from a height h is given by




The horizontal distance traveled by the water before its hits the ground is given by,




The extrema (maxima/minima) of l lies at,






Also at this value of h, it can be verified that the second derivative is negative indicating a maxima.

The distance traveled by the water for this value of h is given by substituting h = H/2 in l and is given by H.

Irodov Problem 1.318

The fluid pressure at the bottom of the container, just above the hole is given by the sum of pressures due to the columns of kerosene and water given by,



Let the atmospheric pressure be Po.

The fluid just above the hole at the bottom is assumed to be still in other words, velocity of the fluid just above the hole is 0.

Just below the hole, say water gushes out with a speed v. The fliud is now flowing into a region of of atmospheric pressure.

Applying Bernoulli's equation we have,

Irodov Problem 1.317

The streamlines of the gas are depicted by the straight line arrows indicated in the figure. Consider the a line in the path of the gas ABC. At points between A through B along this line the velocity of the gas is v. However, along point between B to C, the velocity of the gas is 0, since it has nowhere to flow.

Bernoulli's equation must apply to all points along a line ABC. Let the pressure of the gas in the region AB be P1 and that in the region BC (inside the pilot tube) be P2.

Hence, we have,








The total amount of flow is given by,