Thank you for your reply.
I know that the probability distribution of the sum of two or more random variables is the convolution of their individual pdf's, but as far as I know this is only valid for independent random variables. While ##E(aX+bY)=aE(X)+bE(Y)## is true in general, right?.
1. Homework Statement
Show that the expectation operator E() is a linear operator, or, implying:
E(a\bar{x}+b\bar{y})=aE(\bar{x})+bE(\bar{y})
2. Homework Equations
E(\bar{x})=\int_{-\infty}^{+\infty}xf_{\bar{x}}(x)dx
With f_{\bar{x}} the probability density function of random variable...
1. Homework Statement
1: Determine the wall shear stress that acts at the lower side of the plate.
2: Determine the force Fx that is needed to give the plate a speed of u = 1m/s.
3: Determine the speed V, that is leaves an air jet that blows against the plate and which creates the same force...
Thank you for your reply.
But now I wonder, how is the mean flow of the element defined? If we look at a flowing liquid (for example water), now we can theoretically draw a fluid element and give it a velocity U, but how can we determine what U should be?
Is it wrong to say that the velocity...
Good day,
In my book, the following definition for flow velocity is given:
So summarized, the flow velocity at a point in space is the velocity of an infinitesimally small fluid element as it sweeps through that point. But now my question; how is the velocity of an infinitesimally small...
1. Homework Statement
Consider the following implicit scheme:
y_{n+1}=y_{n}+\frac{\Delta t}{2}\left [f(y_{n+1})+f(y_{n})]
By linearization one can obtain an explicit scheme which is an approximation to this - with approximation error O(\Delta t^{3})
2. Homework Equations
The solution...
Good day,
I don't understand the following:
\frac{d^{2}}{dt^{2}}\int_{0}^{t}(t-\epsilon )\phi (\epsilon)d\epsilon=\phi''(t)
All I know is:
\frac{d^{2}}{dt^{2}}\int_{0}^{t}(t-\epsilon )\phi (\epsilon)d\epsilon=\frac{d^{2}}{dt^{2}}\int_{0}^{t}t \cdot \phi...
1. Homework Statement
Take the Inverse Laplace Transform of: Y(s)=\frac{1}{\tau s+1}\cdot \frac{1}{s}
2. The attempt at a solution
I know:
L^{-1}(\frac{1}{\tau s+1})=\frac{1}{\tau}e^{\frac{-t}{\tau}}
and:
L^{-1}({\frac{1}{s}})=1
But how to continue?
Hello,
1st order autonomous, homogeneous differential equation have the general form:
\dot{x}(t)=ax(t)
It can be shown that the unique solution is always:
x(t)=e^{at}x(t_{0})
I don't get this, could anyone help me?
Thanks!
Thank you for your answer.
Because I have to make quite a lot of graphs with broken y-axis, I am looking for an easier method. The method of the website will take quite some time when I have to make 20 graphs with broken y-axis.
Thank you for your replies.
All the information I have got considering this practice situation:
Information written down on a form will be put in a database. The information in the database can be correct (match the information written on the form) or can be incorrect (do not match the...
1. Homework Statement
With what program (freeware) can I draw a graph with broken y-axis.
An example of what I want:
I know that this is possible by using Excel, but just in a very cumbersome way, right?
Thanks in advance.
1. Homework Statement
What formula do I need to find the confidence interval, when I have got:
- Number of samples
- Level of Confidence
- The assumed (1st guess) accuracy
2. Homework Equations
I found the following equation online: µ = z * [p * (1 - p) / n] ^ (-1/2)
3. The...
1. Homework Statement
Explain why the distance between the centroid and the centre of pressure for a plane submerged fluid decreases as the depth of fluid increases.
I know that the centre of pressure for a plane submerged fluid is located below the centroid because pressure increases with...
1. Homework Statement
Prove that:
sinh(3x)=3sinh(x)+4sinh^{3}(x)
2. The attempt at a solution
I know that:
sinh(3x)=0.5(e^{3x}-e^{-3x})
and:
3sinh(x)=1.5(e^{x}-e^{-x})
But I have no idea how to rewrite 4sinh^{3}(x) in exponential form...
1. Homework Statement
A body when tested in air of density 1.18 kg/m3 and dynamic viscosity 1.52x10^-5 Pas at a velocity of 35 m/s was found to produce a resistance of 250 N. A similarly shaped body 10 times longer than the original was tested in water of dynamic viscosity 1x10^-3 Pas...
1. Homework Statement
A fluid of density 867 kg/m3 flows through a circular duct of diameter 40.60 mm with a mass flow rate of 14.63 kg/s. The fluid velocity in m/s is?
2. Homework Equations
mass flow rate [kg/s] = density [kg/m3] x velocity [m/s] x area [m]
3. The Attempt at a Solution...