Balance these equations.

$$\\$$

(a)

$$\mathrm{CaC_2(s)}+\mathrm{H_2O(l)}\rightarrow\mathrm{Ca(OH)_2(s)}+\mathrm{C_2H_2(g)}$$

(b)

$$\mathrm{(NH_4)_2Cr_2O_7(s)}\rightarrow\mathrm{\mathrm{Cr_2O_3(s)}}+\mathrm{N_2(g)}+\mathrm{H_2O(g)}$$

(c)

$$\mathrm{CH_3NH_2(g)}+\mathrm{O_2(g)}\rightarrow\mathrm{CO_2(g)}+\mathrm{N_2(g)}+\mathrm{H_2O(g)}$$

A turbine receives $450 \mathrm{ft}^3 / \mathrm{sec}$ of water from a $6-\text{ft}$-diameter pipe at a pressure of $120 ~\mathrm{psi}$ and delivers $10000 \mathrm{~kW}$. The pressure in the $7 \frac{1}{2}$-ft-diameter exit pipe is $18\ \text{psi}$. Calculate the turbine efficiency.

Oil flows into a mixing tank through pipe $A$ with an average velocity of $6 \mathrm{~m} / \mathrm{s}$, and glycerin flows into the tank through pipe $B$ at $3 \mathrm{~m} / \mathrm{s}$. Calculate the average density at which the mixture flows out through the pipe at $C$. Assume uniform mixing of the fluids occurs within the $4 \mathrm{~m}^3$ tank. Take $\rho_o=880 \mathrm{~kg} / \mathrm{m}^3$ and $\rho_{g l y}=1260 \mathrm{~kg} / \mathrm{m}^3$.

A water system is used in a laboratory to study flow in a smooth pipe. To obtain a reasonable range, the maximum Reynolds number in the pipe must be $100,000$ . The system is supplied from an overhead constant-head tank. The pipe system consists of a square-edged entrance, two $45^{\circ}$ standard elbows, two $90^{\circ}$ standard elbows, and a fully open gate valve. The pipe diameter is $15.9 \mathrm{~mm}$, and the total length of pipe is $9.8 \mathrm{~m}$. Estimate the minimum height of the supply tank above the pipe system discharge to reach the desired Reynolds number.

Classify each number as one or more of the following: natural number, whole number, integer, rational number, or irrational number.

$$\pi,-3, \frac{2}{9}, \sqrt{9}, 1 . \overline{3},-\sqrt{2}$$

Determine whether each number is an integer, a rational number, an irrational number, a prime number, or a real number.

$$\frac{5}{\sqrt{7}}, \frac{5}{7}, 31,-2 \frac{1}{2}, 4.235653907493,51,0.888 \ldots$$

Oil with kinematic viscosity v = 7.5 $\times 10^{−4}$ ft$^{2}$/s flows at 45 gpm in a 100-ft-long horizontal drawn-tubing pipe of 1 in. diameter. By what percentage ratio will the energy loss increase if the same flow rate is maintained while the pipe diameter is reduced to 0.75 in.?

During a plant visit, it was detected that a 12-m-long section of a 12-cm-diameter steam pipe is completely exposed to the ambient air. The temperature measurements indicate that the average temperature of the outer surface of the steam pipe is $75^{\circ} \mathrm{C}$ when the ambient temperature is $5^{\circ} \mathrm{C}$. There are also light winds in the area at $25 \mathrm{~km} / \mathrm{h}$. The emissivity of the outer surface of the pipe is $0.8$, and the average temperature of the surfaces surrounding the pipe, including the sky, is estimated to be $0^{\circ} \mathrm{C}$. Find the amount of heat lost from the steam during a 10-h-long work day.

Steam is supplied by a gas-fired steam generator that has an efficiency of 80 percent, and the plant pays $\$ 1.05 /$ therm of natural gas. If the pipe is insulated and 90 percent of the heat loss is saved, determine the amount of money this facility will save a year as a result of insulating the steam pipes. Consider the plant operates every day of the year for $10 \mathrm{~h}$. State your assumptions.

An incompressible liquid with negligible viscosity and density $\rho=850 \mathrm{~kg} / \mathrm{m}^3$ flows steadily through a horizontal pipe. The pipe cross-section area linearly varies from $100 \mathrm{~cm}^2$ to $25 \mathrm{~cm}^2$ over a length of $2 \mathrm{~m}$. Develop an expression for and plot the pressure gradient and pressure versus position along the pipe, if the inlet centerline velocity is $1 \mathrm{~m} / \mathrm{s}$ and inlet pressure is $250 \mathrm{kPa}$.

Two wrenches are used to tighten the pipe. If $P=$ $300 \mathrm{~N}$ is applied to each wrench, determine the maximum torsional shear stress developed within regions $A B$ and $B C$. The pipe has an outer diameter of $25 \mathrm{~mm}$ and inner diameter of $20 \mathrm{~mm}$. Sketch the shear stress distribution for both cases.

A circular metal pipe has a wall thickness of 10 mm and an inner diameter of 10 cm. The pipe’s outer surface is subjected to a uniform heat flux of $5 kW/m^2$ and has a temperature of $500^\circ C.$ The metal pipe has a variable thermal conductivity given as $k(T) = k_0 (1 + \beta T),$ where $k_0 = 7.5 W/m \cdot K, \beta = 0.0012 K^{-1},$ and T is in K. Determine the inner surface temperature of the pipe.

A pipe of length 8.0 m is open at one end and closed at the other. The speed of sound is

$$320 \mathrm { ms } ^ { - 1 }$$

. Which is the lowest frequency of a standing wave that can be established within this pipe? A.

$$5.0 \mathrm { Hz }$$

B.

$$10 \mathrm { Hz }$$

C.

$$15 \mathrm { Hz }$$

D.

$$30 \mathrm { Hz }$$

Kacey and Starr found that if 3 times a number is decreased by 5 and this difference is doubled, the result is 14 less than twice the number. What is the number? doubled, the result is 14 less than twice the number. What is the number?

A 0.3-m-diameter pipe is connected to a 0.02-m-diameter pipe, and both are rigidly held in place. Both pipes are horizontal with pistons at each end. If the space between the pistons is filled with water, what force will have to be applied to the larger piston to balance a force of 90 N applied to the smaller piston? Neglect friction.