Tutorial Sheet#1
description
Transcript of Tutorial Sheet#1
![Page 1: Tutorial Sheet#1](https://reader036.fdocuments.in/reader036/viewer/2022082520/5695d0d21a28ab9b02940320/html5/thumbnails/1.jpg)
7212019 Tutorial Sheet1
httpslidepdfcomreaderfulltutorial-sheet1 11
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