91Ó°ÊÓ

(a) Show that the flow speed measured by a venturi meter (see Fig. 10-29) is given by the relation

\({{\bf{v}}_{\bf{1}}}{\bf{ = }}{{\bf{A}}_{\bf{2}}}\sqrt {\frac{{{\bf{2}}\left( {{{\bf{P}}_{\bf{1}}}{\bf{ - }}{{\bf{P}}_{\bf{2}}}} \right)}}{{{\bf{\rho }}\left( {{\bf{A}}_{\bf{1}}^{\bf{2}}{\bf{ - A}}_{\bf{2}}^{\bf{2}}} \right)}}} \).

(b) A venturi meter is measuring the flow of water; it has a main diameter of \({\bf{3}}{\bf{.5\;cm}}\) tapering down to a throat diameter of \({\bf{1}}{\bf{.0\;cm}}\). If the pressure difference is measured to be \({\bf{18\;mm - Hg}}\), what is the speed of the water entering the venturi throat?

A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a \({\bf{7}}{\bf{.0}}\;{\bf{cm}}\)-diameter hose delivering \({\bf{420}}\;{\bf{L/min}}\)through a \({\bf{0}}{\bf{.75}}\;{\bf{cm}}\)-diameter nozzle?

A viscometer consists of two concentric cylinders, \({\bf{10}}{\bf{.20}}\;{\bf{cm}}\) and \({\bf{10}}{\bf{.60}}\;{\bf{cm}}\)in diameter. A liquid fills the space between them to a depth of \({\bf{12}}{\bf{.0}}\;{\bf{cm}}\). The outer cylinder is fixed, and a torque of \({\bf{0}}{\bf{.024}}\;{\bf{m}} \cdot {\bf{N}}\) keeps the inner cylinder turning at a steady rotational speed of \({\bf{57}}\;{\bf{rev/min}}\). What is the viscosity of the liquid?

A rowboat floats in a swimming pool, and the level of the water at the edge of the pool is marked. Consider the following situations. (i) The boat is removed from the water. (ii) The boat in the water holds an iron anchor which is removed from the boat and placed on the shore. For each situation, the level of the water will,

(a) Rise.

(b) Fall.

(c) Stay the same.

(II) A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g. What is the specific gravity of this other fluid?

Will an ice cube float in a glass of alcohol? Why or why not?

What diameter must a \({\bf{15}}{\bf{.5}}\;{\bf{m}}\)-long air duct have if the ventilation and heating system is to replenish the air in a \({\bf{8}}{\bf{.0}}\;{\bf{m \times 14}}{\bf{.0}}\;{\bf{m \times 4}}{\bf{.0}}\;{\bf{m}}\) room every \({\bf{15}}{\bf{.0}}\;{\bf{min}}\)? Assume the pump can exert a gauge pressure of \({\bf{0}}{\bf{.710 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{atm}}\).

(II) Assuming a constant pressure gradient, if blood flow is reduced by 65%, by what factor is the radius of a blood vessel decreased?

(III) A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein (Fig. 10–55). The inside diameter of the 25-mm-long needle is 0.80 mm, and the required flow rate is \(2.0\;{\rm{c}}{{\rm{m}}^3}\) of blood per minute. How high h should the bottle be placed above the needle? Obtain \(\rho \) and \(\eta \) from the Tables. Assume the blood pressure is 78 torr above atmospheric pressure.

Figure 10-55

(I) If the force \(F\) needed to move the wire in Fig. 10–34 is \(3.4 \times {10^{ - 3}}\;{\rm{N}}\), calculate the surface tension \(\gamma \) of the enclosed fluid. Assume \(l = 0.070\;m\).