A $D_0 = 8-m$-diameter tank is initially filled with water 2 m above the center of a D = 10-cm-diameter valve near the bottom. The tank surface is open to the atmosphere, and the tank drains through $a_L = 80-m$-long pipe connected to the valve. The friction factor of the pipe is given to be f = 0.015, and the discharge velocity is expressed as $V=\sqrt{rac{2 g z}{1.5+f L/ D}}$ where z is the water height above the centerof the valve. Determine (a) the initial discharge velocity from the tank and (b) the time required to empty the tank. The tank can be considered to be empty when the water level drops to the center of the valve.

When a generator is used to produce electric current, the resulting electric energy originates from which source? $(a)$ The generator's magnetic field. $(b)$ Whatever rotates the generator's axle. $(c)$ The resistance of the generator's coil. $(d)$ Back emf. $(e)$ Empty space.

Use a rational equation to solve the exercise.

If one pipe can fill a pool in $a$ hours and a second pipe can empty the pool in $b$ hours, write a formula for the time, $x$, in terms of $a$ and $b$, for the number of hours it takes to fill the pool with both of these pipes open.

Two farmers are standing on opposite sides of a very large empty field that is $510 . \mathrm{m}$ across. One farmer yells out some instructions, and $1.50 \mathrm{~s}$ pass until the sound reaches the other farmer. What is the temperature of the air?

One pipe can fill a pond in 3 weeks, and a second pipe can fill it in 5 weeks. However, evaporation and seepage can empty the pond in 10 weeks. If both pipes are used, how long will it take to fill the pond?

A large container holds 5 gallons of water. It begins leaking at a constant rate. After 10 minutes, the container has 3 gallons of water left.

a. At what rate is the water leaking?

b. After how many minutes will the container be empty?

Two farmers are standing on opposite sides of a very large empty field that is $510 \mathrm{~m}$ across. One farmer yells out some instructions, and $1.5 \mathrm{~s}$ pass until the sound reaches the other farmer. What is the temperature of the air?

In each of the following sentences, circle the collective noun. If the pronoun in each sentence does not agree with its antecedent, cross it out and write the correct pronoun above it. If the pronoun already agrees with its antecedent, write C above it.

Example: A $\boxed{\text{{swarm}}}$ of bees hovered over $\overset{\textit{\color{#c34632}{its}}}{\sout{\text{their}}}$ nest.

Beneath the surface of the water, a school of fish made its way toward shore.

In this exercise, write an equation of the direct variation described.

Water is flowing into a swimming pool at the rate of 25 gallons per minute. The number of gallons of water in the pool, g, is directly proportional to the number of minutes, m, that the pool has been filling from when it was empty.

Two identical point charges are fixed to diagonally opposite corners of a square that is 0.500 m on a side. Each charge is

$$+ 3.0 \times 10 ^ { - 6 } \mathrm { C }$$

How much work is done by the electric force as one of the charges moves to an empty corner?

An empty vial weighs $55.32 \mathrm{~g}$.
(b) How much would the vial weigh if it were filled with water $\left(d=0.997 \mathrm{~g} / \mathrm{cm}^3\right.$ at $\left.25^{\circ} \mathrm{C}\right)$ ?

Suppose that s and t are empty stacks and a, b, c, and d are objects. What do the stacks contain after the following sequence of operations executes?

s.push(a);
s.push(b);
s.push(c);
t.push(d);
t.push(s.pop());
t.push(s.peek());
s.push(t.pop());
t.pop();

A 2000-liter cistern is empty when water begins flowing into it (at t=0) at a rate (in L/min) given by Q'(t)=

$$3 \sqrt { t }$$

, where t is measured in minutes. How much water flows into the cistern in 1 hour?

In a particular crystal, the highest occupied band is full. The crystal is transparent to light of wavelengths longer than 295 nm but opaque at shorter wavelengths. Calculate, in electron-volts, the gap between the highest occupied band and the next higher (empty) band for this material.