Chapter 4, Problem 4.21P

(a)

Interpretation Introduction

Interpretation:

The velocity of the plunger of a needle is to be determined without leakage.

Concept Introduction:

The flow rate of the serum in the needle can be given by the principle of mass conservation as mass flow rate is same, in and out of the needle. The equation for mass flow rate is,

  $\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}\text{=}\text{ρ×A×V}\mathrm{.......}\text{(1)}$

  $\begin{array}{l}\text{ρ}\text{is}\text{the}\text{density}\text{of serum}\\ \text{A}\text{is}\text{the}\text{area}\text{of}\text{needle}\text{at}\text{a}\text{point}\\ \text{V}\text{is}\text{the}\text{velocity}\text{at}\text{a}\text{point}\end{array}$

In terms of volumetric flow rate, mass flow rate is,

  $\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}\text{=}\text{ρ×Q}\mathrm{.......}\text{(2)}$

Q is the volumetric flow rate.

(b)

Interpretation Introduction

Interpretation:

The velocity of the plunger of a needle is to be determined with leakage.

Concept Introduction:

The flow rate of the serum in the needle can be given by the principle of mass conservation as mass flow rate is same, in and out of the needle. The equation for mass flow rate is,

  $\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}\text{=}\text{ρ×A×V}\mathrm{.......}\text{(1)}$

  $\begin{array}{l}\text{ρ}\text{is}\text{the}\text{density}\text{of serum}\\ \text{A}\text{is}\text{the}\text{area}\text{of}\text{needle}\text{at}\text{a}\text{point}\\ \text{V}\text{is}\text{the}\text{velocity}\text{at}\text{a}\text{point}\end{array}$

In terms of volumetric flow rate, mass flow rate is,

  $\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}\text{=}\text{ρ×Q}\mathrm{.......}\text{(2)}$

Q is the volumetric flow rate.