Fluid mechanics problem ### Problem Statement9. A conical funnel of half-angle θ is filled to some initial height h₀ with a fluid. At time t = 0, the drain plug is removed and the fluid drains through a hole (with area a) in the bottom of the funnel. Assume that the drain hole area is small compared to the fluid surface area.### Questions**a. Fill in the following table**The dependent variable in this problem is the drain time, t_D:| Independent Variable | If the Independent Variable (with all other parameters held constant) | Your Prediction From Physical Intuition: Does t_D increase (↑) or decrease (↓) ? | Analysis Prediction: | Does Your Prediction Match the Analysis Prediction: ||---------------------------------|:----------------------------------------------------------------------:|:--------------------------------------------------------------------------------:|:----------------------:|:--------------------------------------------:|| Funnel half-angle θ | ↑ | | | || Initial fluid height h₀ | ↑ | | | || Drain hole area a | ↑ | | | || Gravitational Acceleration g | ↑ | | | |**b. Find an expression for the fluid height h(t) as a function of time.***Hint: The way in which this problem differs from the draining tank in class is that the tank area is no longer constant with height. You must find an equation for the tank area A = f(h).***c. Find an expression for the funnel drain time.**### DiagramThe diagram illustrates a conical funnel with the following features:- \( \theta \): The half-angle of the funnel.- \( h \): The height of the fluid at any given time.- \( h = 0 \): The bottom level of the funnel.- \( h_0 \): The initial height of the fluid.``` L / \ / \\ θ \_____/ / h ```Line Diagrams:- The left and right slants of the funnel are depicted.- A horizontal line marks \( h_0 \), the initial height.- \( h \) represents the height of the fluid column at an arbitrary time.- \( \theta \), the half-angle of the funnel, is denoted in the figure.

(a) Independent variable If the independent variable (with all other parameters held constant)…

9. A conical funnel of half-angle 0 is filled to some initial height họ with a fluid. At time t = 0 the drain plug is removed and the fluid drains through a hole (with area a) in the bottom of the funnel. Assume that the drain hole area is small compared to the fluid surface area.

9. A conical funnel of half-angle 0 is filled to some initial height họ with a fluid. At time t = 0 the drain plug is removed and the fluid drains through a hole (with area a) in the bottom of the funnel. Assume that the drain hole area is small compared to the fluid surface area.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: Refer to Fig. 9-36. The angle of static friction between the block with mass M and the plane is d.…

Q: Make an isometric drawing based on the flowchart of the figure, where: PSA GEN = Pressure Swing…

A: Hey dear):-can upload the question again . It is incomplete now .thank you ):-Explanation:

Q: Problem 3: Smoke and Steam One of the most enduring images of the Industrial Revolution is a steam…

Q: A 4.8 m long from fixed point, 0.5 m wide and assumed a thickness of 30 mm throughout a springboard…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: A. What is the coefficient of friction for a sphere of radius 0.37 um? (the viscosity of water is…

A: The coefficient of friction for a sphere moving through a viscous fluid like water can be calculated…

Q: Problem 1: HD-based Ch 7 & MSH-based Ch 3: a solution of unknown origin. Based on the shear rate and…

A: A) From the given table, a graph of shear stress and strain rate is From the graph, it is clear…

Q: Calculate the critical design loads applied to the Stirling E ation and provide a stress analysis on…

A: In order to find critical design load we need to equate thermal strss with reactive force per unit…

Q: Write a a brief note on eccentric impact.

A: Eccentric impact takes place when the line of the mass of the center of two bodies not coincide with…

Q: What does sliding' or slipping condition means velocities are the same in the normal direction…

A: Given:What does sliding' or slipping condition means velocities are the same in the normal direction…

Q: 1. Draw a graph relating dilatant and thixiotropic fluids in terms of torque and viscosity versus…

A: In dilatent fluids, with increase in the velocity, torque and viscosity increases. And for…

Q: Define viscosity of a fluid.

A: Viscosity is a property of fluids.

Q: What term describes a numerical value that can be applied to a dimensional constraint in a technical…

A: Variation process arranging approach is some of the time called an information recovery strategy.…

Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

Fluid mechanics problem

### Problem Statement

9. A conical funnel of half-angle θ is filled to some initial height h₀ with a fluid. At time t = 0, the drain plug is removed and the fluid drains through a hole (with area a) in the bottom of the funnel. Assume that the drain hole area is small compared to the fluid surface area.

### Questions

**a. Fill in the following table**

The dependent variable in this problem is the drain time, t_D:

| Independent Variable | If the Independent Variable (with all other parameters held constant) | Your Prediction From Physical Intuition: Does t_D increase (↑) or decrease (↓) ? | Analysis Prediction: | Does Your Prediction Match the Analysis Prediction: |
|---------------------------------|:----------------------------------------------------------------------:|:--------------------------------------------------------------------------------:|:----------------------:|:--------------------------------------------:|
| Funnel half-angle θ | ↑ | | | |
| Initial fluid height h₀ | ↑ | | | |
| Drain hole area a | ↑ | | | |
| Gravitational Acceleration g | ↑ | | | |

**b. Find an expression for the fluid height h(t) as a function of time.**

*Hint: The way in which this problem differs from the draining tank in class is that the tank area is no longer constant with height. You must find an equation for the tank area A = f(h).*

**c. Find an expression for the funnel drain time.**

### Diagram

The diagram illustrates a conical funnel with the following features:

- \( \theta \): The half-angle of the funnel.
- \( h \): The height of the fluid at any given time.
- \( h = 0 \): The bottom level of the funnel.
- \( h_0 \): The initial height of the fluid.

```
L
/ \
/ \
\ θ \_____/ /
h
```

Line Diagrams:
- The left and right slants of the funnel are depicted.
- A horizontal line marks \( h_0 \), the initial height.
- \( h \) represents the height of the fluid column at an arbitrary time.
- \( \theta \), the half-angle of the funnel, is denoted in the figure.

Branch of science that deals with the stationary and moving bodies under the influence of forces.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

F-m question. Provide right answer
________ form of governing equations are solved at the grid points to find the unknown fluid quantities? ( this is fill in the blank) circle final answer
viscosity and density of olive oil at 20C. use perrys table
An organic oil was produced from the plant materials and animal fats. Tests showed that the oil behaved differently in cold weather as compared to its performance in hot condition and as such it was graded as SAE 15W-40. Based on its rheological behavior, what kind of fluid is the oil produced? A. NEWTONIAN B. NON-NEWTONIAN C. IDEAL FLUID
Question / Calculate the critical design loads applied to the Stirling Engine when in operation and provide a stress analysis on the piston .use a factor of safety of 5. Assume outside temperature (bottom plate) is -233 degC and an internal PC board (top plate) is 85 degC ? Figure 1.1 show measurement to help you