itisarainyday/ml_classifier_bert_training · Datasets at Hugging Face

0 stringlengths 10 969	label int64 0 1
Use Ackeret's theory to estimate the pressure coefficient on each side of a flat plate in a flow at latex0 at an incidence angle of latex1 .	0
A steel is used in a steam turbine pipe which operates at latex0 .	0
Show that for very light damping ( latex6 ) the initial state of the transient solution satisfies latex7 , latex8 .	1
A partition in the tank ensures that the oil stays on the left.	0
After analysing the readings from a strain gauge rosette mounted on a latex0 diameter shaft which was subjected to bending and torsion, it was found that the principal strains latex1 and latex2 were latex3 , latex4 and that latex1 was inclined at latex6 to the axis of the shaft.	0
Show that, if the cylinder is closed-ended, it will be predicted to fail at latex6 if the Von Mises criterion is used.	1
Explain the differences between bed-load and suspended-load sediment transport.	1
Its rate of climb is latex1 .	0
Figure (a): A snooker cue balancing on its tip.	0
What is the value of latex4 at the bottom surface and the top surface of the water?	1
The Bernoulli equation says that the total head, latex0 on a streamline is constant and can be defined as: latex1 Show what the three terms on the right-hand side represent.	1
Calculate the separation of the bright fringes on a screen 2 m from the slits.	1
\[Boas 4.53] Given latex0 , latex1 , latex2 , find latex3 (using the chain rule).	1
Of the two solutions in part (a), consider the one closest to latex7 .	1
An entire, real reciprocating engine, accounting for the air and fuel entering and the exhaust gas mixture leaving?	1
For a first order process with gain latex0 and time constant latex1 , determine a control gain latex2 in a unity feedback control system, necessary to speed up the step response to latex3 .	1
Explicitly calculate when the points latex2 , latex3 , and latex4 pass a station latex12 downstream of the origin.	1
Determine an expression for the length latex4 of the region in which latex5 .	1
Considering for now only the line latex4 , show that your answer to (b) simplifies to an ODE for latex9 .	1
Calculate the product latex8 .	1
Calculate the values of latex3 and latex4 from this data set using linear regression (use Excel if you want).	1
It must withstand an axial compressive load of latex0 .	0
An infinity of solutions latex0 latex1 latex2 latex3	0
Explain the method and state the underlying assumptions you consider to be of importance.	1
What would be the concentration of caffeine in the coffee drinker's blood after latex13 , given that the elimination constant latex3 is latex15 ?	1
For large (but not infinite) latex1 , this is a good model of a diffraction grating.	0
Consider the following equation: latex0 where latex1 is a variable and latex2 is a parameter (i.e it doesn't depend on latex1 ).Write an expression for the solution to this equation.	1
The real part is latex1 and has units of length.	0
(L8): Use Gaussian elimination to solve the system of equations below (Note: these are the same equations as Q1, so you know the type of solution to expect).	1
When gas and latex0 excess air are supplied at latex1 , the temperature of the flue gases leaving the boiler is latex2 .	1
% display the two initial values and print their difference fprintf(' '); fprintf('Initial values for X1 and X2: '); fprintf('X1 = %+18.16f ',X1); fprintf('X2 = %+18.16f ',X2); fprintf('----------------------------- '); fprintf('diff = %+20.14e ',X2-X1); % ......................................................................... % .................................................... iterate the tent map for n = 1:nit if X1 <= 0.5 X1 = 2X1; else X1 = 2 - 2X1; end if X2 <= 0.5 X2 = 2X2; else X2 = 2 - 2X2; end end % ......................................................................... % ................. display the two final values and print their difference fprintf(' '); fprintf('Values for X1 and X2 after %s iterations: ',num2str(nit)); fprintf('X1 = %+18.16f ',X1); fprintf('X2 = %+18.16f ',X2); fprintf('----------------------------- '); fprintf('diff = %+20.14e ',X2-X1); % .........................................................................m	1
A pulley, latex0 , of diameter latex1 and moment of inertia latex2 is connected by a belt to a pulley, latex3 , of diameter, latex4 .	0
One end of a light string of length latex0 is attached to a fixed point at latex1 .	0
Why are both sets of lines parallel to the dry-bulb axis?	1
Determine the transfer function latex0 of the two following circuits, with latex1 , latex2 , latex3 and latex4 :	1
Use these expressions to find latex12 and latex13 in terms of latex4 and latex18 .	1
It is essential that the robot, when approaching the eye, does not exceed the target position, otherwise it will perforate the eye irreversibly.	0
Carbon dioxide, which can be treated as a perfect gas, flows steadily at a rate of latex0 through a heat exchanger where it is cooled at constant pressure (i.e with negligible friction) from latex1 to latex2 .	0
A wide river is dredged to make it more navigable.	0
What is the order in which the lamps turn on in the car's rest frame?	1
Find the transformation matrix that transforms the resulting shape into a rectangle latex7 .	1
Given that the tower is 60 m high, what is the separation of the two balls when the first hits the ground?	1
Select a resistor which, in combination with a latex5 capacitor, will reduce the ripple by latex8 .	1
Recalculate the energy falling on the panel if it is now placed flat on the ground at a location with latitude latex9 .	1
If not, what was wrong with the approach taken in this question?	1
If the blade speed is latex2 , calculate the velocity and flow angle relative to the rotor blades.	1
A scale model of an aeroplane is to be tested in a wind tunnel at latex0 .	0
Find latex2 for latex4 .	1
Ignore the possibility of buckling failure modes and the weight of the beam.	0
Two point charges of value latex0 are fixed in position at latex1 and latex2 .	0
The circuit shown below is used in an automatic camera to measure light intensity.	0
Compute the coefficient of friction, latex4 .	1
By matching the transfer operators of the op-amp stage and its block diagram representation, derive expressions for A and B.	1
A device to measure the dynamic viscosity of a fluid is called a viscometer.	0
The frame has a mass latex4 with centre of gravity latex5 .	0
What is depth of the plate into the water?	1
In this problem we will assume that all three principal moments are distinct latex1 .	0
An isolated air bubble of radius latex0 is in water.	0
Note that Zener diodes can be used in series to achieve non-standard voltages (i.e their Zener voltages can be added, while the same current flows through each one).	0
In lectures, you saw that the total laboratory-frame kinetic energy of two particles is the sum of their kinetic energy in the centre-of-mass frame and the kinetic energy of the centre of mass in the laboratory frame.	0
(This is the mechanics question from the 2020 exam.	0
Note: The solutions below should be given in their simplest form.	0
Now, let's repeat this exercise using complex numbers (which should be much easier).	0
The video linked from the image below shows an Imperial College physics student doing a simple experiment with a pendulum.	0
The rotor exit tangential gas velocity component (magnitude and sign).	0
Assume the following: 1.	0
If you're short of time, leave this for another day.Show that: latex10 Verify that the wall-normal velocity component latex11 may be related to the stream function as follows: latex12 Show that: latex13 Based on the above results, show that the momentum equation from the boundary-layer equations eventually reduce to the Blasius equation: latex14 Convert the boundary conditions for latex4 and latex11 to a set of boundary conditions applied to latex5 and/or latex18 .	1
Show that: latex11	1
It accelerates down to the ground at C, rises to D, and descends to E, which is at the same height as A.	0
Again ignoring time dilation, use the exponential function of particle decay to find the average fraction of muons predicted to reach the Earth's surface.	1
Consider steady flow between two stationary, flat plates as illustrated below.	0
Anti-aliasing filters are used to remove signals that could cause aliasing.	0
Using the Blasius solution, estimate the shear stress on the fin at the midpoint.	1
Which of the following properties are scalars?	1
An aircraft flies due North at latex0 ground speed.	0
Consider the fluid contained in a cylindrical container as shown in the figure below.	0
In the chemical reaction latex0 , there is an intermediate step where the latex1 and latex2 molecules combine to form an activated complex latex3 x latex4 \cdot latex5 ^{-1} latex6 \text{NO} + \text{O}_3 latex7 6.022 \times 10^{23} latex8 [\text{NO--O}_3]^{\ast} latex9 m_u \approx 1.66 \times 10^{-27}$).	0
(L6) Solve: latex0	1
If not, when are they closest together and what is their distance of closest approach?	1
(Hint: start from Lecture 13 and non-dimensionalising the equations, but with the appropriate pressure scale.	0
Power lost as a fraction of the initial kinetic power:	0
The container undergoes a rotation around its vertical axis ( latex1 ) at a constant angular velocity, latex2 .	0
Use the shock polar to answer the following questions (estimate to about latex0 ).	1
Suppose that you were lucky enough to take the following picture of a Super Hornet flying slightly above the speed of sound at sea level.	0
Show, by substitution, that in the case of critical damping, the solution is latex19	0
The specific volume of the fluid with a temperature of latex14 and a pressure of latex15 .	0
Use Mohr's circle only.	0
How much energy is dissipated in friction as the record slips on the turntable?	1
Determine the transfer function between the movement of the mass, latex1 , with respect to ground, and the displacement of the cart latex3 .	1
Hence find latex14 in terms of latex0 .	1
Find the velocity field of the flow, assuming that it is a purely circulating motion, that is latex11 , latex12 and latex13 .	1
Calculate the fuel gas volume flow rate required to generate latex7 of dry saturated steam at latex8 bar (absolute) from feed water at latex9 .	1
iii) latex12 ?	1
Determine the Mach number at the nozzle exit ( latex1 ) Determine the pressure at the nozzle exit ( latex2 ).	1
It is falling through a fluid of density latex2 and viscosity latex3 .	0
In the antidune system the water surface is in phase with the bed configuration with a larger water depth at the antidune crest than at the antidune trough.	0
(Take rotation in the clockwise direction to be positive) Find the percentage of energy lost in the collision.	1
Analyse the experiment mathematically, assuming for simplicity that the string has been replaced by a light but stiff rod so that the starting angle can range from latex3 to latex4 radians.	1
The gyroscope rotor is mounted on a horizontal shaft fixed across the vehicle frame, parallel with the rear axle and has a mass moment of inertia latex0 about its spin axis.	0
Estimate the thrust capacity.	1

Use Ackeret's theory to estimate the pressure coefficient on each side of a flat plate in a flow at latex0 at an incidence angle of latex1 .

0

A steel is used in a steam turbine pipe which operates at latex0 .

0

Show that for very light damping ( latex6 ) the initial state of the transient solution satisfies latex7 , latex8 .

1

A partition in the tank ensures that the oil stays on the left.

0

After analysing the readings from a strain gauge rosette mounted on a latex0 diameter shaft which was subjected to bending and torsion, it was found that the principal strains latex1 and latex2 were latex3 , latex4 and that latex1 was inclined at latex6 to the axis of the shaft.

0

Show that, if the cylinder is closed-ended, it will be predicted to fail at latex6 if the Von Mises criterion is used.

1

Explain the *differences between bed-loa*d and suspended-load sediment transport.

1

Its rate of climb is latex1 .

0

**Figure (a)**: A snooker cue balancing on its tip.

0

What is the value of latex4 at the bottom surface and the top surface of the water?

1

The Bernoulli equation says that the total head, latex0 on a streamline is constant and can be defined as: latex1 Show what the three terms on the right-hand side represent.

1

Calculate the separation of the bright fringes on a screen 2 m from the slits.

1

**\[Boas 4.53]** Given latex0 , latex1 , latex2 , find latex3 (using the chain rule).

1

Of the two solutions in part (a), consider the one closest to latex7 .

1

An entire, real reciprocating engine, accounting for the air and fuel entering and the exhaust gas mixture leaving?

1

For a first order process with gain latex0 and time constant latex1 , determine a control gain latex2 in a unity feedback control system, necessary to speed up the step response to latex3 .

1

Explicitly calculate when the points latex2 , latex3 , and latex4 pass a station latex12 downstream of the origin.

1

Determine an expression for the length latex4 of the region in which latex5 .

1

Considering for now only the line latex4 , show that your answer to (b) simplifies to an ODE for latex9 .

1

Calculate the product latex8 .

1

Calculate the values of latex3 and latex4 from this data set using linear regression (use Excel if you want).

1

It must withstand an axial compressive load of latex0 .

0

An infinity of solutions latex0 latex1 latex2 latex3

0

Explain the method and state the underlying assumptions you consider to be of importance.

1

What would be the concentration of caffeine in the coffee drinker's blood after latex13 , given that the elimination constant latex3 is latex15 ?

1

For large (but not infinite) latex1 , this is a good model of a diffraction grating.

0

Consider the following equation: latex0 where latex1 is a variable and latex2 is a parameter (i.e it doesn't depend on latex1 ).Write an expression for the solution to this equation.

1

The real part is latex1 and has units of length.

0

**(L8)**: Use Gaussian elimination to solve the system of equations below (**Note**: these are the same equations as Q1, so you know the type of solution to expect).

1

When gas and latex0 excess air are supplied at latex1 , the temperature of the flue gases leaving the boiler is latex2 .

1

% display the two initial values and print their difference fprintf(' '); fprintf('Initial values for X1 and X2: '); fprintf('X1 = %+18.16f ',X1); fprintf('X2 = %+18.16f ',X2); fprintf('----------------------------- '); fprintf('diff = %+20.14e ',X2-X1); % ......................................................................... % .................................................... iterate the tent map for n = 1:nit if X1 <= 0.5 X1 = 2*X1; else X1 = 2 - 2*X1; end if X2 <= 0.5 X2 = 2*X2; else X2 = 2 - 2*X2; end end % ......................................................................... % ................. display the two final values and print their difference fprintf(' '); fprintf('Values for X1 and X2 after %s iterations: ',num2str(nit)); fprintf('X1 = %+18.16f ',X1); fprintf('X2 = %+18.16f ',X2); fprintf('----------------------------- '); fprintf('diff = %+20.14e ',X2-X1); % .........................................................................m

1

A pulley, latex0 , of diameter latex1 and moment of inertia latex2 is connected by a belt to a pulley, latex3 , of diameter, latex4 .

0

One end of a light string of length latex0 is attached to a fixed point at latex1 .

0

Why are both sets of lines parallel to the dry-bulb axis?

1

Determine the transfer function latex0 of the two following circuits, with latex1 , latex2 , latex3 and latex4 :

1

Use these expressions to find latex12 and latex13 in terms of latex4 and latex18 .

1

It is essential that the robot, when approaching the eye, does not exceed the target position, otherwise it will perforate the eye irreversibly.

0

Carbon dioxide, which can be treated as a perfect gas, flows steadily at a rate of latex0 through a heat exchanger where it is cooled at constant pressure (i.e with negligible friction) from latex1 to latex2 .

0

A wide river is dredged to make it more navigable.

0

What is the order in which the lamps turn on in the car's rest frame?

1

Find the transformation matrix that transforms the resulting shape into a rectangle latex7 .

1

Given that the tower is 60 m high, what is the separation of the two balls when the first hits the ground?

1

Select a resistor which, in combination with a latex5 capacitor, will reduce the ripple by latex8 .

1

Recalculate the energy falling on the panel if it is now placed flat on the ground at a location with latitude latex9 .

1

If not, what was wrong with the approach taken in this question?

1

If the blade speed is latex2 , calculate the velocity and flow angle relative to the rotor blades.

1

A scale model of an aeroplane is to be tested in a wind tunnel at latex0 .

0

Find latex2 for latex4 .

1

Ignore the possibility of buckling failure modes and the weight of the beam.

0

Two point charges of value latex0 are fixed in position at latex1 and latex2 .

0

The circuit shown below is used in an automatic camera to measure light intensity.

0

Compute the coefficient of friction, latex4 .

1

By matching the transfer operators of the op-amp stage and its block diagram representation, derive expressions for A and B.

1

A device to measure the dynamic viscosity of a fluid is called a *viscometer*.

0

The frame has a mass latex4 with centre of gravity latex5 .

0

What is depth of the plate into the water?

1

In this problem we will assume that all three principal moments are distinct latex1 .

0

An isolated air bubble of radius latex0 is in water.

0

Note that Zener diodes can be used in series to achieve non-standard voltages (i.e their Zener voltages can be added, while the same current flows through each one).

0

In lectures, you saw that the total laboratory-frame kinetic energy of two particles is the sum of their kinetic energy in the centre-of-mass frame and the kinetic energy of the centre of mass in the laboratory frame.

0

(This is the mechanics question from the 2020 exam.

0

**Note**: The solutions below should be given in their simplest form.

0

Now, let's repeat this exercise using complex numbers (which should be much easier).

0

The video linked from the image below shows an Imperial College physics student doing a simple experiment with a pendulum.

0

The rotor exit tangential gas velocity component (magnitude and sign).

0

Assume the following: 1.

0

If you're short of time, leave this for another day.Show that: latex10 Verify that the wall-normal velocity component latex11 may be related to the stream function as follows: latex12 Show that: latex13 Based on the above results, show that the momentum equation from the boundary-layer equations eventually reduce to the Blasius equation: latex14 Convert the boundary conditions for latex4 and latex11 to a set of boundary conditions applied to latex5 and/or latex18 .

1

Show that: latex11

1

It accelerates down to the ground at C, rises to D, and descends to E, which is at the same height as A.

0

Again ignoring time dilation, use the exponential function of particle decay to find the average fraction of muons predicted to reach the Earth's surface.

1

Consider steady flow between two stationary, flat plates as illustrated below.

0

Anti-aliasing filters are used to remove signals that could cause aliasing.

0

Using the Blasius solution, estimate the shear stress on the fin at the midpoint.

1

Which of the following properties are scalars?

1

An aircraft flies due North at latex0 ground speed.

0

Consider the fluid contained in a cylindrical container as shown in the figure below.

0

In the chemical reaction latex0 , there is an intermediate step where the latex1 and latex2 molecules combine to form an activated complex latex3 x latex4 \cdot latex5 ^{-1} latex6 \text{NO} + \text{O}_3 latex7 6.022 \times 10^{23} latex8 [\text{NO--O}_3]^{\ast} latex9 m_u \approx 1.66 \times 10^{-27}$).

0

**(L6)** Solve: latex0

1

If not, when are they closest together and what is their distance of closest approach?

1

(Hint: start from Lecture 13 and non-dimensionalising the equations, but with the appropriate pressure scale.

0

Power lost as a fraction of the initial kinetic power:

0

The container undergoes a rotation around its vertical axis ( latex1 ) at a constant angular velocity, latex2 .

0

Use the shock polar to answer the following questions (estimate to about latex0 ).

1

Suppose that you were lucky enough to take the following picture of a Super Hornet flying slightly above the speed of sound at sea level.

0

Show, by substitution, that in the case of critical damping, the solution is latex19

0

The specific volume of the fluid with a temperature of latex14 and a pressure of latex15 .

0

Use Mohr's circle *only*.

0

How much energy is dissipated in friction as the record slips on the turntable?

1

Determine the transfer function between the movement of the mass, latex1 , with respect to ground, and the displacement of the cart latex3 .

1

Hence find latex14 in terms of latex0 .

1

Find the velocity field of the flow, assuming that it is a purely circulating motion, that is latex11 , latex12 and latex13 .

1

Calculate the fuel gas volume flow rate required to generate latex7 of dry saturated steam at latex8 bar (absolute) from feed water at latex9 .

1

iii) latex12 ?

1

Determine the Mach number at the nozzle exit ( latex1 ) Determine the pressure at the nozzle exit ( latex2 ).

1

It is falling through a fluid of density latex2 and viscosity latex3 .

0

In the antidune system the water surface is in phase with the bed configuration with a larger water depth at the antidune crest than at the antidune trough.

0

*(Take rotation in the clockwise direction to be positive)* Find the percentage of energy lost in the collision.

1

Analyse the experiment mathematically, assuming for simplicity that the string has been replaced by a light but stiff rod so that the starting angle can range from latex3 to latex4 radians.

1

The gyroscope rotor is mounted on a horizontal shaft fixed across the vehicle frame, parallel with the rear axle and has a mass moment of inertia latex0 about its spin axis.

0

Estimate the thrust capacity.

1