Water water everywhere: except in your canteen.
So why are the rangers so insistent upon carrying water? Maybe because your body is 75% water. We lose water when we breathe, when we urinate, or when we sweat. Hiking in the desert (which the Canyon is) you will lose a lot of water through sweat. If you are dripping sweat, it is ineffective at cooling your person.
If you lose 2.5% of your body weight in sweat, you will feel thirsty (duh!), and lose your appetite. Hikers may lose 30% of their performance, and most of us don't have much performance to spare while we are climbing out of the Canyon.
At 5% you may feel groggy, sleepy, and nauseous. At 10% to 15%, muscles become spastic, vision may dim, urination may become painful, and after 15%, you may die.
For a 200 pound person, 2% body weight is 4 pounds. That is two liters of water. In extreme conditions, a hiker can sweat off 1.5 to 2 liters of water per hour.
No matter what you may have read in desert survival manuals, or seen on TV, you cannot train yourself to hike with less water. An athlete who is acclimated begins to sweat SOONER and sweats twice as much than a person who is not acclimated. An acclimated desert hiker loses ten times less salt through perspiration than a non-desert hiker.
A desert hiker begins to sweat as soon as he or she starts to hike. A non desert hiker will not begin to sweat until the body core temperature has risen to 100 degrees.
The big Catch 22 here is that if you drink too much and don't eat, you flush out salt. You will feel the same symptoms as dehydration, but you know you have drunk enough water. The impress-your-friends term for this is hyponatremia, and it is just as dangerous as dehydration. Usually it occurs because people don't feel like eating when it is hot, or because they have a limited amount of space in their day pack, so they carry water but not enough food.
As a basic rule, drink 500-100 milliliters per hour (a liter is just about a quart). Consume 500 to 1500 mg of salt per hour. Consume 500-1500 calories per hour.
Electrolyte replacement drinks and goo packets are not sufficient. In point of fact, relying only on electrolytes is a leading cause of hyponatremia. Salty junk food is your friend.
It is physically impossible to carry enough water to keep you alive during the heat of the summer. You must then control the amount of water you lose. So hike during the coolest part of the day (before 10 AM and after 4 PM), rest in the shade, and wet yourself down given every opportunity to do so. Drink before you get thirsty. Eat salty snacks whenever you rest.