Answered: A cup is a cylinder with a diameter of…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter15: Fluid Mechanics

Section: Chapter Questions

Problem 25P: A 10.0-kg block of metal measuring 12.0 cm by 10.0 cm by 10.0 cm is suspended from a scale and...

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Question

A cup is a cylinder with a diameter of 9.87cm and is 30cm tall. The hole is 1.44 from the bottom of the cup and has a diameter of 0.254cm. The cup sits at the edge of a 0.912m tall table.
A.) Find the velocity of the water leaving the hole when the cup is full.
B.) How far away from the table does the water hit the floor?

Expert Solution

Step 1

Given :

Height H = 30 cm = 0.3 m

$H - h = 1.44 c m$ = 0.0144 m

diameter of cup = 9.87 cm = 0.0987 m

hole diameter =0.254 cm = 0.00254 m

Length of Table = 0.912 m

(a) Velocity of efflux :

$v = \sqrt{2 g h}$

h= 30 - 1.44 cm= 28.56 cm

Plug value of g and h we get velocity with which water leave from hole

$v = \sqrt{2 \times 9.8 \times 0.2856} = \sqrt{5.597} = 2.36 m / s$

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