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Chapter 6: Problem 76

A horizontal axisymmetric jet of air with 0.4 in. diameter strikes a stationary vertical disk of 7.5 in. diameter. The jet speed is \(225 \mathrm{ft} / \mathrm{s}\) at the nozzle exit. A manometer is connected to the center of the disk. Calculate (a) the deflection, if the manometer liquid has \(\mathrm{SG}=1.75,(\mathrm{b})\) the force exerted by the jet on the disk, and (c) the force exerted on the disk if it is assumed that the stagnation pressure acts on the entire forward surface of the disk. Sketch the streamline pattern and plot the distribution of pressure on the face of the disk.

Short Answer

Expert verified
Jet is causing the fluid in the manometer to deflect by a certain amount. Forces exerted on the disk by the jet and by considering the stagnation pressure acting over the whole area were computed. The streamline pattern of the flow and the distribution of pressure on the disk's surface were also visually represented. Critical thinking and application of fluid dynamics principles were crucial in solving this problem.

Step by step solution

01

Calculate the Deflection

The deflection in the manometer is given by \( \Delta h = \frac{v^{2}}{2g} \frac{1}{SG - 1} \), where v is the velocity of air, g is the acceleration due to gravity and SG is the specific gravity of the manometer liquid. Given \( v = 225 ft/s, SG = 1.75 \) and \( g = 32.2 ft/s^2 \), substitute these values in to get the deflection.
02

Calculate the Force Exerted by the Jet on the Disk

The force exerted by the jet is given by F = \(\rho Q v \), where 蟻 is the density of the air, Q is the volumetric flow rate of the air, and v is the velocity of air. We know \( 蟻 = 0.002378 slug/ft^3 \) and V = \( \pi (D^2)/4 \times v \), where D is the jet diameter. Substitute the given and computed values into the formula to find F.
03

Calculate the Force considering Stagnation Pressure

The force when considering the stagnation pressure is F = P_s 脳 A where P_s is the stagnation pressure and A is the area of the disk. P_s = \( 蟻v^2/2 + 蟻gh\) where h is the height above some reference point (we can take h as zero here as there is no such height specified). The area A is \( \pi (D^2)/4 \) where D is the diameter of the disk. Substitute the values into the formulas to find F.
04

Sketch the Streamline Pattern and Plot the Pressure Distribution

The streamline pattern can be sketched by following the motion of the air particles from the jet nozzle to the disk. The pressure distribution on the face of the disk can be plotted by considering points along the radius of the disk and evaluating the pressure at these points using the Bernoulli's equation. Keep in mind that pressure would be highest at the center and would decrease as we move towards the edge.

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