Recent questions tagged numerical-answers

A vector field$$\mathbf{B}(x, y, z)=x \; \hat{\imath}+y \; \hat{\jmath}-2 z \; \hat{\mathrm{k}}$$is defined over a conical region having height $h=2$, base radius $r=3$ a...

A linear transformation maps a point $(x, y)$ in the plane to the point $(\hat{x}, \hat{y})$ according to the rule$$\hat{x}=3 y, \quad \hat{y}=2 x .$$Then, the disc $x^2+...

The value of $k$ that makes the complex-valued function$$f(z)=e^{-k x}(\cos 2 y-i \sin 2 y)$$analytic, where $z=x+i y$, is __________. (Answer in integer)

The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force $\mathbf{P}$. The belt wraps ar...

Consider a counter-flow heat exchanger with the inlet temperatures of two fluids $(1$ and $2)$ being $T_1$, in $=300 \mathrm{~K}$ and $T_2$, in $=350 \mathrm{~K}$. The he...

A spherical ball weighing $2 \mathrm{~kg}$ is dropped from a height of $4.9 \mathrm{~m}$ onto an immovable rigid block as shown in the figure. If the collision is perfect...

Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is $A$. The fluid inside th...

In an ideal orthogonal cutting experiment (see figure), the cutting speed $V$ is $1 \mathrm{~m} / \mathrm{s}$, the rake angle of the tool $\alpha=5^{\circ}$, and the shea...

A $\text{CNC}$ machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw, which in turn moves a nut horizontally ...

A very large metal plate of thickness $d$ and thermal conductivity $k$ is cooled by a stream of air at temperature $T_{\infty}=300 \mathrm{~K}$ with a heat transfer coeff...

Consider the second-order linear ordinary differential equation$$x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=0, \quad x \geq 1$$with the initial conditions$$y(x=1)=6,\lef...

The initial value problem$$\frac{d y}{d t}+2 y=0, \quad y(0)=1$$is solved numerically using the forward Euler's method with a constant and positive time step of $\Delta t...

The atomic radius of a hypothetical face-centered cubic (FCC) metal is $(\sqrt{2} / 10) \; \mathrm{nm}$. The atomic weight of the metal is $24.092 \mathrm{~g} /$ mol. Tak...

A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The samp...

A coordinate measuring machine (CMM) is used to determine the distance between Surface $\text{SP}$ and Surface $\text{SQ}$ of an approximately cuboidal shaped part. Surfa...

A solid part (see figure) of polymer material is to be fabricated by additive manufacturing $\text{(AM)}$ in square-shaped layers starting from the bottom of the part wor...

An optical flat is used to measure the height difference between a reference slip gauge $\text{A}$ and a slip gauge $\text{B}$. Upon viewing via the optical flat using a ...

Ignoring the small elastic region, the true stress $(\sigma)-\operatorname{true}$ strain $(\varepsilon)$ variation of a material beyond yielding follows the equation $\si...

The area moment of inertia about the $y$-axis of a linearly tapered section shown in the figure is __________ $\mathrm{m}^4$.(Answer in integer)

A cylindrical bar has a length $L=5 \mathrm{~m}$ and cross section area $S=10 \mathrm{~m}^{2}$. The bar is made of a linear elastic material with a density $\rho=2700 \ma...

A cylindrical transmission shaft of length $1.5 \mathrm{~m}$ and diameter $100 \mathrm{~mm}$ is made of a linear elastic material with a shear modulus of $80 \mathrm{GPa}...

Consider a mixture of two ideal gases, $\mathrm{X}$ and $\mathrm{Y}$, with molar masses $\bar{M}_{\mathrm{X}}=10 \mathrm{~kg} / \mathrm{kmol}$ and $\bar{M}_{\mathrm{Y}}=2...

The velocity field of a certain two-dimensional flow is given by$\boldsymbol{V}(x, y)=k(x \hat{\imath}-y \hat{\jmath})$where $k=2 \mathrm{~s}^{-1}$. The coordinates $x$ a...

Consider a unidirectional fluid flow with the velocity field given by$$V(x, y, z, t)=u(x, t) \hat{\imath}$$where $u(0, t)=1$. If the spatially homogeneous density field v...

The figure shows two fluids held by a hinged gate. The atmospheric pressure is $P_a=100 \mathrm{kPa}$. The moment per unit width about the base of the hinge is __________...

An explosion at time $t=0$ releases energy $\text{E}$ at the origin in a space filled with a gas of density $\rho$. Subsequently, a hemispherical blast wave propagates ra...

Consider the definite integral$$\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$$Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using ...

A structural member under loading has a uniform state of plane stress which is usual notations is given by $\sigma _{x} = 3P, \sigma _{y} = -2P$ and $\tau_{xy} = \sqrt{2}...