# Applying the integral form of impulse momentum

The theoretical relationship for impact of jet on a stationary surface can be established by considering integral forms of continuity and momentum equations. For one dimensional steady incompressible fluid flow condition, the mass conservation equation is given by continuity equation as shown in equation 1.

(1)

Where Q is the volumetric flow rate,

and are velocities at section 1 and 2 respectively, and

and are cross-sectional area of pipe at section 1 and 2.

Figure 1 shows the fluid flow parameters and the geometric parameters for the derivation of theoretical expression of force on stationary surfaces due to jet of water. , is the velocity of jet by which it strikes the surface and deflects away in radially outward direction with velocity of at an angle of . The dashed lines represent the control volume considered for the derivation. It is assumed that the friction between water and the impact surface is negligible and the jet velocity does not vary. Under this assumption and from equation 1 we can write

(2)

Also in horizontal direction, since the flow and the surface is symmetrical, the horizontal reaction will be zero.

Figure 1: Geometric and fluid parameters for impact of jet experiment

Applying the integral form of impulse momentum equation we get:

(3)

Where is the reaction force in vertical direction. Now, using equation 2 this relationship can be reduced to:

(4)

Here:

Thus Equation 4 can be written as:

(5)

Equation 5 represents the theoretical expression for computing the impact force on a stationary surface due to a vertical jet of liquid.

3. EXPERIMENTAL APPARATUS

The schematic diagram for the experimental arrangement is shown in figure 2 and the apparatus diagram is shown in Figure 3. The water is supplied from the pump to a vertical pipe, which ends in a nozzle. This produces a jet of water which strikes the vane, in form of a flat plate or a hemispherical cup shape surface.

Figure 2: Schematic for the experiment arrangement.

This arrangement of the nozzle and the vane is contained in a transparent cylinder. This cylinder ends in an outlet, which flows directly to the collection tank. The vane is attached to a lever carrying jockey weight and is restrained by an arrangement of light spring. The jockey weight can be adjusted at a desired length over the lever to bring back the vane to its original balanced position.

Picture 479

Figure 3: Jet-Impact Measuring Bench.

4. PROCEDURE

Step 1: In the first step the lever was set to a balanced position by placing the jockey weight at zero and adjusting the nuts over spring arrangement.

Step 2: Now, jockey weight, diameter of the nozzle, vane height above the nozzle tip and the distance of vane Centre to lever pivot were noted down.

Step 3: Now water was allowed through the nozzle by opening the flow control valve. As the jet stroked the surface the vane moved upwards. Now additional weights were placed bring back the lever to its original balanced position.

Step 4: At this position the flow rate was noted down from the collection tank by measuring taken to collect a fixed weight of water collected in tank, using a stopwatch.

Step 5: The procedure was repeated to get another set of readings at same flow rate. Step 6: Steps 1 to 5 were repeated to get readings for four more flow rates.

Step 7: Steps 1 to 6 were repeated for hemispherical vane.

5. RESULTS

This section of the report explains the results of the experiment and its comparison with the expected theoretical results. The experiment was performed over the apparatus mentioned in section 3 of the report. Appendix shows the data recorded as per step 2 of section 4.

Based on the steps mentioned in section 4, Table 1 and Table 2 shows the experimental force values for flat surface and Cup shaped surface respectively.