Tutorial Sheet#1
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7/21/2019 Tutorial Sheet#1 http://slidepdf.com/reader/full/tutorial-sheet1 1/1 B.Tech APE/APE2 Tutorial # 1 Solution of Algebraic and Transcendental Equations VI 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 + − = 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, 0.0820 litre atm/(deg mole). The volume of 1 mole of a perfect gas at standard conditions (1 atm, 273 K) is 22.415 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 1.36 0.0318 3.78 0.0441 2. The Beattie-Bridgeman equation of state = + + + is a three parameter extension of the ideal gas law. Using = −1.06, = 0.057, = −0.0001, find the volume of 1 mole of a gas at P=25 atm , and T=293 K. The constant R=0.082 litre-atm/K-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 − − + 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 / , = 0.35, = 9.8 / . 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 = − −ℎ√2ℎ −ℎ . Determine h given r=2m, L=5m, and V=8 m 3 . 5. Bernoulli’s equation for fluid flow in an open channel with a small bump is given by the equation + = + +H . Determine h for the following parameters: Q = 1.2 / = Volume rate of flow g = 9.81 / = gravitational acceleration b = 1.8 m = width of the channel ℎ = 0.6 m = upstream water level H = 0.075 m = height of bump h = water level above the bump ***
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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
