   Chapter 9, Problem 43P

Chapter
Section
Textbook Problem

A jet of water squirts out horizontally from a hole near the bottom of the tank shown in Figure P9.43. If the hole has a diameter of 3.50 mm, what is the height h of the water level in the tank? Figure P9.43

To determine
The height h of the water level in the tank.

Explanation
At first, the time for water to reach the ground by considering it as a projectile motion using Newton’s equations of motion is Δy=v0yt+(1/2)ayt2 with initial downward speed of water is v0y=0m/s and the height of the hole from the ground is 1.00m and the negative sign is because of the assumption of the hole is being at y=0m . The time is t=2(Δy)/ay . The horizontal speed of water is v2=v0x=Δx/t=Δx/2(Δy)/ay . Assume points 1 and 2 are assigned for top of the tank and for level of the hole. Both points have same pressure that is P1=P2=Patm and the speed of the water at top of the tank is v10m/s   Now Bernoulli’s equation is written for this problem as ρgy1=(1/2)ρv22+ρgy2y1y2=v22/2g

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