Bernoulli Equation in Fluid Dynamics

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Questions and Answers

What is the primary reason for high failure rates in extension-base removable partial dentures (RPDs)?

  • Poor plaque control around the abutments
  • Inadequate extension of the denture base
  • Suboptimal framework design
  • Difference in hard tooth and soft tissue support leading to abutment movement (correct)
  • Lack of patient recall appointments for adjustments

During abutment evaluation for an extension-base RPD, why might radiographs alone be insufficient?

  • Radiographs can be misleading; clinical examination with a periodontal probe is essential. (correct)
  • Radiographs always reveal adequate bone support.
  • Radiographs clearly show the need for splinting.
  • Radiographs accurately depict periodontal health.
  • Radiographs provide a complete view of root morphology.

Which of the following pre-prosthetic surgical procedures is LEAST likely to be necessary for an extension-base RPD?

  • Extraction of impacted third molars
  • Creating space for denture components
  • Tori removal (correct)
  • Block repositioning with surgery
  • Tuberosity reduction

What is a rationale for ensuring complete coverage of the available supporting area, such as the pear-shaped pad and buccal shelf, during impression taking for an extension-base RPD?

<p>To maximize support and stability of the denture base. (E)</p> Signup and view all the answers

In the context of extension-base RPDs, what is the primary purpose of considering the shape of the roots of potential abutment teeth?

<p>To assess their ability to withstand forces and provide adequate support. (C)</p> Signup and view all the answers

When might a fixed partial denture be considered a possible treatment option during the evaluation of abutments for an extension-base RPD?

<p>When there is an isolated second bicuspid requiring replacement. (A)</p> Signup and view all the answers

Why is the altered cast technique utilized in the context of impression making for extension-base RPDs?

<p>To improve the accuracy of the fit of the denture base to the edentulous ridge. (B)</p> Signup and view all the answers

What is the significance of block repositioning as a pre-prosthetic surgical procedure?

<p>To correct jaw discrepancies and improve the relationship between the arches. (E)</p> Signup and view all the answers

What factor most significantly impacts the long-term success of an extension-base RPD?

<p>The distribution of occlusal forces and the stability of the abutments. (B)</p> Signup and view all the answers

Why is evaluating the need for splinting abutment teeth an important step in planning an extension-base RPD?

<p>To distribute occlusal forces across multiple teeth and improve stability. (A)</p> Signup and view all the answers

Why is the utilization of third molars generally discouraged in pre-prosthetic surgery for removable partial dentures?

<p>Third molars often exhibit unpredictable morphology and position, complicating RPD design and stability. (C)</p> Signup and view all the answers

Which of the following is the MOST important consideration when choosing impression materials for an extension-base RPD?

<p>The ability to accurately record the details of the supporting tissues. (B)</p> Signup and view all the answers

In the context of pre-prosthetic surgery, what is a 'tuberosity trim' designed to achieve?

<p>To create adequate interarch space for the RPD. (C)</p> Signup and view all the answers

Why is a lack of patient recall a factor in the high failure rate of extension-base RPDs?

<p>Because adjustments and maintenance are needed to address changes in the supporting tissues and occlusal relationships. (E)</p> Signup and view all the answers

What is the potential consequence of inadequate denture bases in extension-base RPDs?

<p>Uneven stress distribution, leading to tissue irritation, bone resorption, and instability. (A)</p> Signup and view all the answers

In the context of impression materials used for RPD fabrication, what does 'equal accuracy if handled correctly' imply?

<p>That clinical technique is paramount in achieving optimal results, irrespective of the specific material chosen. (D)</p> Signup and view all the answers

Why is poor design a factor in the high failure rate of extension-base RPDs?

<p>Poor design compromises support, retention, and stability, leading to excessive stress on abutment teeth and tissues. (A)</p> Signup and view all the answers

Why is noting the shape of the roots during abutment evaluation important?

<p>Because root shape can provide an indication of long-term stability and periodontal support. (A)</p> Signup and view all the answers

In impression taking, what is the significance of the pear-shaped pad?

<p>It provides a stable area for support. (C)</p> Signup and view all the answers

What is the main goal of pre-prosthetic surgery?

<p>Creating a more favorable prognosis for the placement of a dental prosthesis. (B)</p> Signup and view all the answers

Flashcards

Primary reason for RPD failure

Difference in hard tooth and soft tissue support, causing tipping, rocking and torquing of abutments.

How to evaluate abutments?

Radiographs can be misleading, so you should use your periodontal probe.

Examples of Pre-Prosthetic Surgery

Surgical block repositioning, tuberosity trims, designs for limited space.

Rationale for complete RPD coverage

Complete coverage of available supporting area - especially pear-shaped pad and buccal shelf.

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Block repositioning with surgery

Surgical procedure to reposition bone or soft tissue to improve the foundation for a dental prosthesis.

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Tuberosity trims

The removal or reshaping of excess tissue on the maxillary tuberosities to create adequate space for the denture.

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Altered cast technique

A dental technique where a custom tray is made to accurately record the edentulous ridge, improving denture fit.

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Study Notes

Bernoulli Equation

  • Describes fluid behavior with relationships between pressure, velocity, and elevation.
  • Formula: $\frac{P_1}{\rho} + \frac{V_1^2}{2} + gz_1 = \frac{P_2}{\rho} + \frac{V_2^2}{2} + gz_2$

Bernoulli Equation Assumptions

  • Flow is steady state.
  • Fluid is incompressible
  • No energy loss due to friction.
  • Flow occurs along a streamline.

Friction Correction to Bernoulli Equation

  • Accounts for energy loss due to friction.
  • Formula: $\frac{P_1}{\rho} + \frac{V_1^2}{2} + gz_1 = \frac{P_2}{\rho} + \frac{V_2^2}{2} + gz_2 + h_f$
  • $h_f$ represents the head loss due to friction.

Pump Work in Bernoulli Equation

  • Includes the energy added to fluid by a pump.
  • Formula is: $\frac{P_1}{\rho} + \frac{V_1^2}{2} + gz_1 + W_p = \frac{P_2}{\rho} + \frac{V_2^2}{2} + gz_2 + h_f$
  • $W_p$ is the work done by the pump.

Turbine Work in Bernoulli Equation

  • Accounts for energy extracted from fluid by a turbine.
  • Equation: $\frac{P_1}{\rho} + \frac{V_1^2}{2} + gz_1 = \frac{P_2}{\rho} + \frac{V_2^2}{2} + gz_2 + h_f + W_t$
  • $W_t$ is the work done by the turbine.

Example: Pumping Water Through a Pipe

  • Water at $20^\circ C$ is pumped at a rate of 2 $\frac{Kg}{s}$.
  • Properties of water at $20^\circ C$: $\rho$ = 998 $\frac{Kg}{m^3}$, $\mu$ = 0.001 $Pa \cdot s$
  • A motor supplies 3 Kw of power to the pump.
  • Inlet pressure $P_1$ is 1 atmosphere
  • Pipe is 2-inch schedule 40.
  • Schedule 40 2-inch pipe dimensions: $ID = 0.0525 m$, $A = 0.002165 m^2$
  • Goal: Determine the pressure at $P_2$?

Mass Balance

  • Mass balance is used to find the velocity.
  • $\dot{m} = \rho V A$
  • $2 \frac{Kg}{s} = 998 \frac{Kg}{m^3} \cdot V \cdot 0.002165 m^2$
  • $V = 0.9255 \frac{m}{s}$

Applying Bernoulli Equation

  • $\frac{P_1}{\rho} + \frac{V_1^2}{2} + gz_1 + W_p = \frac{P_2}{\rho} + \frac{V_2^2}{2} + gz_2 + h_f$
  • $V_1 = V_2$
  • $z_1 = 0, z_2 = 2 m$
  • Simplified equation: $\frac{P_1}{\rho} + W_p = \frac{P_2}{\rho} + gz_2 + h_f$

Pump Work Calculation

  • $W_p = \frac{P_{shaft}}{\dot{m}} = \frac{3000 \frac{J}{s}}{2 \frac{Kg}{s}} = 1500 \frac{J}{Kg}$

Head Loss Calculation

  • $h_f = \frac{fLV^2}{2D}$
  • Friction factor needs to be determined.

Reynold's Number Calculation

  • Used to determine the nature of the flow, laminar or turbulent
  • $Re = \frac{\rho V D}{\mu} = \frac{998 \frac{Kg}{m^3} \cdot 0.9255 \frac{m}{s} \cdot 0.0525m}{0.001 Pa \cdot s} = 48440$

Friction Factor Determination

  • Assume smooth pipe: $f = 0.004$
  • $h_f = \frac{0.004 \cdot 20 m \cdot (0.9255 \frac{m}{s})^2}{2 \cdot 0.0525m} = 0.65 \frac{m^2}{s^2}$

Solving for $P_2$

  • $\frac{101325 Pa}{998 \frac{Kg}{m^3}} + 1500 \frac{J}{Kg} = \frac{P_2}{998 \frac{Kg}{m^3}} + 9.81 \frac{m}{s^2} \cdot 2m + 0.65 \frac{m^2}{s^2}$
  • $P_2 = 150000 Pa = 1.48 \ atm$

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