Question

Prob-3 A boat is held stationary by a cable attached to a pier. A firehose directs a spray of 5°C water at a speed of V=75 m/s. If the allowable load on the cable is 5 kN, calculate the mass flow rate of the water jet. What is the corresponding diameter of the water jet? Dom.

Answer 1

Here, the tension on the cable is given as 5kN. The tensile force is acting in the horizontal direction since the cable is horizontal as it can be seen in the figure. The boat is stationary. That means, this tension is balanced by the horizontal reaction, the water jet exerts on the boat. We are required to find out the mass flow rate of the water jet and the corresponding diameter of the water jet. Both can be found out by writing the force balance equation in the x direction.

At 5°C, Wotan density, p=1000 kg/m3 Tension, T on the cable = 5.ok N Balancing forces in the X-disection T=mV cos60° -(1) m Mass flow rate of water in kg/s V = Water speed = 75m/s from ean. (1) m T 5810² 75 x cos 60° = 133.333 kg/s - W cos 60° mi ni =p (d) V 133.333 = 1000x (d)x75 d =0.04.76m d = 4.76cm Where d' is the diameter of water jet.