Question

A horizontal jet of water strikes a vertical surface on a stationary cart that has a mass of 2.8 kg. The jet has a mass flow rate of 0.13 kg/s. The force required to hold the cart in place is 8N. What is the diameter of the nozzle? a. 1.6 mm b. 5.1 mm c. 3.4 mm d. 7.3 mm

Answer 1

Answer:

option a is correct answer i.e. d = 1.6 mm

Explanation:

From conservation principle

force by jet = force required to hold the jet

force by the jet is written as

$force = \dot{m}(v_{1}-v_{2})$

force required to hold the jet = 8N

$\dot{m}(v_{1})\ = 8$

$\dot{m}=0.13 kg/s$

$v_{1} = 61.58 m/s$

we know that mass flow rate is given as

$\dot{m}=\rho Av_{1}$

substituting value to get required  diameter of the nozzle

$0.13=1000*\frac{\pi }{4}d^{2}*61.58$

d = 1.6 mm