Related questions with answers

Liquid flows at steady state at a rate of 2 lb/s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. The liquid specific enthalpy at the inlet is 40.09 Btu/lb and at the exit is 40.94 Btu/lb. The pump requires 3 Btu/s of power to operate. If kinetic energy effects are negligible and gravitational acceleration is $32.174 \: ft/s^2$ , the heat transfer rate associated with this steady- state process is most closely

\begin{array}{l l } \text{(a) 1.04 Btu/s from the liquid to the surroundings}\\ \text{(b) 2.02 Btu/s from the liquid to the surroundings}\\ \text{(c) 3.98 Btu/s from the surroundings to the liquid}\\ \text{(d) 4.96 Btu/s from the surroundings to the liquid}\\ \end{array}

Solve.

5x + 6x \lt -33

Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication operations on $\mathbf{u}=\left(u_{1}, u_{2}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}\right)$ : $\mathbf{u}+\mathbf{v}=\left(u_{1}+v_{1}+1, u_{2}+v_{2}+1\right), \quad k \mathbf{u}=\left(k u_{1}, k u_{2}\right)$ (a) Compute $\mathbf{u}+\mathbf{v}$ and $k \mathbf{u}$ for $\mathbf{u}=(0,4), \mathbf{v}=(1,-3)$ , and k = 2. (b) Show that $(0,0) \neq 0$ . (c) Show that $(-1,-1)=0$ . (d) Show that Axiom 5 holds by producing an ordered pair $-\mathbf{u}$ such that $\mathbf{u}+(-\mathbf{u})=\mathbf{0}$ for $\mathbf{u}=\left(u_{1}, u_{2}\right)$ . (e) Find two vector space axioms that fail to hold.

Question

A flow idealized as a throttling process through a device has
$\begin{array}{l l } \text{(a) $h_{2}>h_{1}$ and $p_{2}>p_{1}$}\\ \text{(b) $h_{2}=h_{1}$ and $p_{2}>p_{1}$}\\ \text{(c) $h_{2}>h_{1}$ and $p_{2}<p_{1}$}\\ \text{(d) $h_{2}=h_{1}$ and $p_{2}<p_{1}$}\\ \end{array}$

Solution

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$\textbf{1.)}$ In a steady-state, steady-flow process, significant changes in pressure and temperature can occur to the fluid, and yet the process will be $\textbf{isenthalpic}$ if there is no transfer of heat to or from the surroundings, no work done on or by the surroundings, and no change in the kinetic energy of the fluid.

$\textbf{2.)}$ If a steady-state, steady-flow process is analysed using a control volume, everything outside the control volume is considered to be the surroundings..

$\textbf{3.)}$ The throttling process is a good example of an $\textbf{isenthalpic process.}$ Consider the lifting of a relief valve or safety valve on a pressure vessel.

$\textbf{4.)}$ The specific enthalpy of the fluid inside the pressure vessel is the same as the specific enthalpy of the fluid as it escapes from the valve.

$\textbf{5.)}$ With a knowledge of the specific enthalpy of the fluid and the pressure outside the pressure vessel, it is possible to determine the temperature and speed of the escaping fluid.

So, the answer is $\textbf{d.)}$ $h_{2}=h_{1}$ and $p_{2}<p_{1}$ , it is isenthalpic process but pressure reduces.