7212019 Tutorial Sheet1

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BTech APEAPE2 Tutorial 1

Solution of Algebraic and Transcendental EquationsVI Semester Instructor Ravi Kiran Maddali

(Solve the following problems by using Bolzano false position Newton Raphson methods)

1 The van der Waals equation of state a simple extension of the ideal gas law discovered in 1873 by the

Dutch physicist Johanes Diderik van der Waals is

+ minus =

where the constants a and b characteristics of the gas are determined experimentally For P in atmospheres

V in liters n in moles and T in kelvins 98316600820 litre atm(deg mole) The volume of 1 mole of a perfect

gas at standard conditions (1 atm 273 K) is 22415 liters Find the volume occupied by 1 mole of the

following gases under standard conditions with given values of a and b correct to 4 decimal places

Gas a B

136 00318

378 00441

2 The Beattie-Bridgeman equation of state = +

+ +

is a three parameter extension of the ideal

gas law Using = minus106 = 0057983137983150983140 = minus00001 find the volume of 1 mole of a gas at P=25 atm

and T=293 K The constant R=0082 litre-atmK-g mole

3 The position of a ball thrown up with a given initial velocity from an initial position subject to air

resistance proportional to its velocity is given by the following equation = + 1 minus

minus + where r is the drag coefficient g is the gravitational constant and

=

is the terminal

velocity Find when the ball hits the ground if = 0 = 20 = 035 = 98

4 The volume V of liquid in a hollow horizontal cylinder of radius r and length L is related to the depth of the

liquid h by = minus minus ℎradic2ℎ minus ℎ Determine h given r=2m L=5m and V=8 m3

5

Bernoullirsquos equation for fluid flow in an open channel with a small bump is given by the equation

+ 983144 = + 983144 + H Determine h for the following parameters

Q = 12 = Volume rate of flow g = 981 = gravitational acceleration

b = 18 m = width of the channel ℎ = 06 m = upstream water level

H = 0075 m = height of bump h = water level above the bump