How to find the derivative for calculating water flow rate?

Click For Summary
SUMMARY

The discussion focuses on calculating the derivative to determine the rate of water flow from a tank through an orifice. The height of the water in the tank is modeled by the equation 2h^(1/2) + (1/23)t - 80^(1/2). The primary question is how to find the rate at which the height decreases when it reaches 8 ft. Participants emphasize the need for a complete equation to properly derive the height's rate of change.

PREREQUISITES
  • Understanding of calculus, specifically derivatives
  • Familiarity with fluid dynamics concepts
  • Knowledge of mathematical modeling of physical systems
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the application of the chain rule in calculus
  • Learn about fluid flow equations and orifice flow dynamics
  • Explore the concept of related rates in calculus
  • Practice solving differential equations related to fluid height changes
USEFUL FOR

Students in calculus, engineers working with fluid dynamics, and anyone involved in mathematical modeling of fluid systems will benefit from this discussion.

miaprincess22
Messages
1
Reaction score
0
This due today!

Water flows from a tank of constant cross-sectional area 56 ft2 through an orifice of constant cross-sectional area 1.5 ft2 located at the bottom of the tank.
Initially the height of the water in the tank was 20 and its height t sec later is given by the following equation.

2h^(1/2) + (1/23)t -80^(1/2)

How fast was the height of the water decreasing when its height was 8 ft? (Round your answer to two decimal places.)

I thought I was just supposed to find the derivative. I keep getting wrong.
 
Last edited:
Physics news on Phys.org
miaprincess22 said:
This due today!

Water flows from a tank of constant cross-sectional area 56 ft2 through an orifice of constant cross-sectional area 1.5 ft2 located at the bottom of the tank.
Initially the height of the water in the tank was 20 and its height t sec later is given by the following equation.

2h^(1/2) + (1/23)t -80^(1/2)

How fast was the height of the water decreasing when its height was 8 ft? (Round your answer to two decimal places.)

I thought I was just supposed to find the derivative. I keep getting wrong.
Yes, you are asked for the derivative of h. One problem you have is that what you give is NOT an "equation"! What is that expression supposed to be equal to? Is 'h' in that formula supposed to be the height?
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
4K
Replies
3
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
2
Views
3K
Replies
11
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K