   Chapter 9, Problem 91AP

Chapter
Section
Textbook Problem

A water tank open to the atmosphere at the top has two small holes punched in its side. one above the other. The holes are 5.00 cm and 12.0 cm above the floor. How high does water stand in the tank if the two streams of water hit the floor at the same plate?

To determine
The height of the water stand in the tank if the two streams hit the floor at the same place.

Explanation

The following figure shows water flowing from a tank.

Explanation: We compare, the water droplet that emerging out from one of the holes with the projectile motion. The component of the speed of the water flow is v0y=0 and v0x=v . The time for the droplet to reach the ground from the height of h is Δy=v0yt+(1/2)ayt2t=(2Δy)/g=2h/g . The horizontal range of the droplet from the base of the tank is R=vt=v2h/g . Hence the two streams hit the floor at the same point with same instant we consider the condition of their ranges as R1=R2v12h1/g=v22h2/gv1=(h2/h1)v2                              (I)

Now we apply Bernoulli’s law for the location mentioned as 1 and 3 such that by assuming v30 ,

Patm+(1/2)ρv12+ρgh1=Patm+0+ρgh3v12=2g(h3h1) (II)

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