   # Imagine the water level in the tank described in Problem 9.38 rises at a rate of 0.1 in/s. Knowing the diameter of the tank is 6 in., what is the average velocity of the water leaving the tank? Express your answer in in/s, ft/s, and m/s. ### Engineering Fundamentals: An Intro...

5th Edition
Saeed Moaveni
Publisher: Cengage Learning
ISBN: 9781305084766

#### Solutions

Chapter
Section ### Engineering Fundamentals: An Intro...

5th Edition
Saeed Moaveni
Publisher: Cengage Learning
ISBN: 9781305084766
Chapter 9, Problem 39P
Textbook Problem
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## Imagine the water level in the tank described in Problem 9.38 rises at a rate of 0.1 in/s. Knowing the diameter of the tank is 6 in., what is the average velocity of the water leaving the tank? Express your answer in in/s, ft/s, and m/s.

To determine

Find the average velocity of the water leaving the tank.

### Explanation of Solution

Given data:

Refer to the given Figure Problem 9.38 in the textbook, which shows the tank is filled by water using pipes 1 and 2.

The water level increases in the rate of 0.1 in/s.

The diameter of the tank is (dtank) 6 in.

Formula used:

Write the expression for the volume flow rate.

Q=VaverageAc

Here,

Ac is cross-sectional area, and

Vaverage is average velocity.

Calculation:

Consider that the constant water density.

From the given figure, write the volume flow rate expression for inlet and outlet volumetric flow rate expressions.

Q1+Q2Q3=Atankchangeintheheightofwatertime

Re-arrange the equation,

Q1+Q2Atankchangeintheheightofwatertime=Q3V1A1+V2A2Atankchangeintheheightofwatertime=V3A3[V1(π4)(d1)2+V2(π4)(d2)2(π4)(dtank)2(0.1ins)=V3(π4)(d3)2=Q3]        [A=π4d2,and[changeintheheightofwater]time=0.1ins]

Substitute 2fts for V1, 1.5fts for V2, 1 in. for d1, 1.75 in. for d2, 1.5 in. for d3, and 6 in. for dtank,

(2fts)(π4)(1in.)2+(1.5fts)(π4)(1.75in.)2(π4)(6in.)2(0.1in.s)=(V3)(π4)(1.5in.)2=Q3{[(2fts)(π4)(1ft12)2+(1

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