Q1. A horizontal water pipe diameter 15 cm converges to 7.5 cm diameter. If the pressures at the...

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Q1.  A horizontal water pipe diameter 15 cm converges to 7.5 cm diameter. If the pressures at the two sections are 4 kgf/cm2, and 1.5 kgf/cm2 respectively, calculate the flow rate of water.    Q2.   A pipe conveys 0.25 kg/s of air at 300 K and under an absolute pressure 2.25 bar. Calculate the minimum diameter of pipe necessary if the flow velocity is limited to 7.5 m/s.    Q3.            Fire services arrived at a site to put out a fire on the   ground floor of a building. The fire chief decided there is no need to turn   on the pump in the fire truck since fire is on lower grounds and nozzle   connection at the end of the hose can be used. The diagram below shows the   arrangement of the firefighting efforts through a hose-pipe connected to the   tank in the truck. The following parameters are known:    (water)            (gauge)             (assuming fully   developed turbulent flow)                                          Listing any assumption(s) you make:      a)   Calculate   the velocity at the nozzle exit ().      b)   Calculate   the pressure at the lowest point in the hose-pipe ().      c)   Determine   the height of water (h) in the tank that provides the   pressure () at location 3. Was the pump required?       d)   If flow was reversed through the   nozzle, find that will result in an   inward velocity of  at location 2.                 Q4.    In a 100 mm diameter horizontal pipe, a venturimeter of 0.5 contraction ratio has been fitted. The head of water on the meter when there is no flow is 3 m (gauge). Find the rate of flow for which the throat pressure will be 2m of water absolute. Discharge coefficient for the meter is 0.97.    Q5.  A jet of water, cross-sectional area 20 cm2, issues with a velocity of 25 m/s and strikes a stationary flat plate held at 30-degree to the axis of jet. Find the force exerted by the jet on the plate, and workout the components of force in the directions normal to the jet. Also find how the discharge gets distributed after striking the plate.    Q6.  A 30 cm diameter pipe carries water under a head of 20 metres with a velocity of 3.5 m/s. If the axis of the pipe turns through 45˚, find the magnitude and direction of the resultant force on the bend    Q7.          A U-tube differential manometer:      a)   is   used upright when pressure difference is large      b)   is   used inverted when pressure difference is small      c)   is   used when pressure difference is large      d)   cannot   be used in inverted position      e)   must   be fitted with a well for sake of accuracy

Samarpeet · Accepted Answer

Q1.
A horizontal water pipe diameter 15 cm converges to 7.5 cm diameter. If the pressures at the two sections are 4 kgf/cm2, and 1.5 kgf/cm2 respectively, calculate the flow rate of water.
Solution:
Q = CdA1V1
Assuming Cd = 0.95
Continuity equation: A1V1= A2V2
		         π/4×152/4 × V1 = π/4×7.52/4 × V2
		         V2= 4V1
Applying bernoulii’s equation P1+ ρgh1+1/2 ρV12= P2+ ρgh2+1/2 ρV22
			 or, 	4+1/2 ×ρV12= 1.5+ 1/2× V22
	 	                     or, 	V22- V12= 2.5×2/ρ
			  or,	(4V1)2- V12= 5/0.001
     			  or,	15 V12	= 5000
			  or,	V1=  18.257 cm/s
Q = A1V1= (0.95 xπ x152/4)× 18.257
Q = 167.879 x 18.257
Q = 3064.966 cm3/s
Q2. 
A pipe conveys 0.25 kg/s of air at 300 K and under an absolute pressure 2.25 bar. Calculate the minimum diameter of pipe necessary if the flow velocity is limited to 7.5 m/s.
Mass of air M = 0.25 kg/s Temperature T = 300-degreeK Pressure P = 2.25 bar P = 225x10^3 pa velocity V = 7.5 m/s
Solution:
m= ρAv= ρ× π/4×D2×v
D = (4m/πρv)1/2
D - internal pipe diameter; m - mass flow rate; ρ - fluid density; v - velocity.
D = [4x0.25/(π x1000x7.5)]1/2
D = 0.00651m = 6.51mm
Q3.
	Fire services arrived at a site to put out a fire on the ground floor of a building. The fire chief decided there is no need to turn on the pump in the fire truck since fire is on lower grounds and nozzle connection at the end of the hose can be used. The diagram below shows the arrangement of the firefighting efforts through a hose-pipe connected to the tank in the truck. The following parameters are known:

Q1. A horizontal water pipe diameter 15 cm converges to 7.5 cm diameter. If the pressures at the two sections are 4 kg f /cm 2 , and 1.5 kg f /cm 2 respectively, calculate the...

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